Relevant bibliographies by topics / Shirshova

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Academic literature on the topic 'Shirshova'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Shirshova"

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Bezhenar, V. F., E. F. Kira, A. S. Turlak, B. N. Novikov, and K. E. Kira. "DMITRY IVANOVICH SHIRSHOV – DOCTOR, SCIENTIST, INNOVATOR (on the 150th anniversary of the birth)." Scientific Notes of the I. P. Pavlov St. Petersburg State Medical University 25, no. 4 (April 21, 2019): 15–20. http://dx.doi.org/10.24884/1607-4181-2018-25-4-15-20.

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IIn 2018, the 150th anniversary of Dmitrii I. Shirshov was celebrated. The article is devoted to Shirshov’s biography and describes his research pathway, the main achievements in obstetrics, gynecology and urogynecology. In addition, the article tells about the characteristic of his clinical and teaching activities.
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Bryant, R. M., L. G. Kovács, and Ralph Stöhr. "Subalgebras of free restricted Lie algebras." Bulletin of the Australian Mathematical Society 72, no. 1 (August 2005): 147–56. http://dx.doi.org/10.1017/s0004972700034936.

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A theorem independently due to A.I. Shirshov and E. Witt asserts that every subalgebra of a free Lie algebra (over a field) is free. The main step in Shirshov's proof is a little known but rather remarkable result: if a set of homogeneous elements in a free Lie algebra has the property that no element of it is contained in the subalgebra generated by the other elements, then this subset is a free generating set for the subalgebra it generates. Witt also proved that every subalgebra of a free restricted Lie algebra is free. Later G.P. Kukin gave a proof of this theorem in which he adapted Shirshov's argument. The main step is similar, but it has come to light that its proof contains substantial gaps. Here we give a corrected proof of this main step in order to justify its applications elsewhere.
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SHNEERSON, L. M. "IDENTITIES AND A BOUNDED HEIGHT CONDITION FOR SEMIGROUPS." International Journal of Algebra and Computation 13, no. 05 (October 2003): 565–83. http://dx.doi.org/10.1142/s0218196703001559.

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We consider two different types of bounded height condition for semigroups. The first one originates from the classical Shirshov's bounded height theorem for associative rings. The second which is weaker, in fact was introduced by Wolf and also used by Bass for calculating the growth of finitely generated (f.g.) nilpotent groups. Both conditions yield polynomial growth. We give the first two examples of f.g. semigroups which have bounded height and do not satisfy any nontrivial identity. One of these semigroups does not have bounded height in the sense of Shirshov and the other satisfies the classical bounded height condition. This develops further one of the main results of the author's paper (J. Algebra, 1993) where the first examples of f.g. semigroups of polynomial growth and without nontrivial identities were given.
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Qiu, Jianjun, and Yuqun Chen. "Gröbner–Shirshov bases for Lie Ω-algebras and free Rota–Baxter Lie algebras." Journal of Algebra and Its Applications 16, no. 10 (September 20, 2017): 1750190. http://dx.doi.org/10.1142/s0219498817501900.

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We generalize the Lyndon–Shirshov words to the Lyndon–Shirshov [Formula: see text]-words on a set [Formula: see text] and prove that the set of all the nonassociative Lyndon–Shirshov [Formula: see text]-words forms a linear basis of the free Lie [Formula: see text]-algebra on the set [Formula: see text]. From this, we establish Gröbner–Shirshov bases theory for Lie [Formula: see text]-algebras. As applications, we give Gröbner–Shirshov bases of a free [Formula: see text]-Rota–Baxter Lie algebra, of a free modified [Formula: see text]-Rota–Baxter Lie algebra, and of a free Nijenhuis Lie algebra and, then linear bases of these three algebras are obtained.
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Tunyaz, Rabigul, and Abdukadir Obul. "Gröbner–Shirshov pair of irreducible modules over quantized enveloping algebra of type An." Journal of Algebra and Its Applications 17, no. 02 (January 23, 2018): 1850035. http://dx.doi.org/10.1142/s0219498818500354.

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In this paper, first, we give a Gröbner–Shirshov pair of finite-dimensional irreducible module [Formula: see text] over [Formula: see text] the quantized enveloping algebra of type [Formula: see text] by using the double free module method and the known Gröbner–Shirshov basis of [Formula: see text] Then, by specializing a suitable version of [Formula: see text] at [Formula: see text] we get a Gröbner–Shirshov basis of [Formula: see text] and get a Gröbner–Shirshov pair for the finite-dimensional irreducible module [Formula: see text] over [Formula: see text].
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Lee, Dong-il. "Gröbner-Shirshov Bases for Exceptional Lie Superalgebras." Algebra Colloquium 22, no. 01 (January 7, 2015): 1–10. http://dx.doi.org/10.1142/s1005386715000024.

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Yilmaz, Erol, Cenap Özel, and Uğur Ustaoğlu. "Gröbner–Shirshov basis and reduced words for affine Weyl group Ãn." Journal of Algebra and Its Applications 13, no. 06 (April 20, 2014): 1450005. http://dx.doi.org/10.1142/s0219498814500054.

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Using Buchberger–Shirshov Algorithm, Composition–Diamond Lemma and partitions of integers we obtain the reduced Gröbner–Shirshov basis of Ãn and classify all reduced words of the affine Weyl group Ãn.
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Zhao, Xiangui, and Yang Zhang. "Gelfand-Kirillov Dimensions of Modules over Differential Difference Algebras." Algebra Colloquium 23, no. 04 (September 26, 2016): 701–20. http://dx.doi.org/10.1142/s1005386716000596.

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Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension of a finitely generated module over a differential difference algebra through a computational method: Gröbner-Shirshov basis method. We develop the Gröbner-Shirshov basis theory of differential difference algebras, and of finitely generated modules over differential difference algebras, respectively. Then, via Gröbner-Shirshov bases, we give algorithms for computing the Gelfand-Kirillov dimensions of cyclic modules and finitely generated modules over differential difference algebras.
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Kalorkoti, K., and I. Stanciu. "Parametrized Gröbner–Shirshov bases." Communications in Algebra 45, no. 5 (October 7, 2016): 1996–2017. http://dx.doi.org/10.1080/00927872.2016.1226875.

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Bokut, L. A., Yuqun Chen, and Abdukadir Obul. "Some new results on Gröbner–Shirshov bases for Lie algebras and around." International Journal of Algebra and Computation 28, no. 08 (December 2018): 1403–23. http://dx.doi.org/10.1142/s0218196718400027.

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We review Gröbner–Shirshov bases for Lie algebras and survey some new results on Gröbner–Shirshov bases for [Formula: see text]-Lie algebras, Gelfand–Dorfman–Novikov algebras, Leibniz algebras, etc. Some applications are given, in particular, some characterizations of extensions of groups, associative algebras and Lie algebras are given.
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Dissertations / Theses on the topic "Shirshova"

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Zhao, Xiangui. "Groebner-Shirshov bases in some noncommutative algebras." London Mathematical Society, 2014. http://hdl.handle.net/1993/24315.

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Groebner-Shirshov bases, introduced independently by Shirshov in 1962 and Buchberger in 1965, are powerful computational tools in mathematics, science, engineering, and computer science. This thesis focuses on the theories, algorithms, and applications of Groebner-Shirshov bases for two classes of noncommutative algebras: differential difference algebras and skew solvable polynomial rings. This thesis consists of three manuscripts (Chapters 2--4), an introductory chapter (Chapter 1) and a concluding chapter (Chapter 5). In Chapter 1, we introduce the background and the goals of the thesis. In Chapter 2, we investigate the Gelfand-Kirillov dimension of differential difference algebras. We find lower and upper bounds of the Gelfand-Kirillov dimension of a differential difference algebra under some conditions. We also give examples to demonstrate that our bounds are sharp. In Chapter 3, we generalize the Groebner-Shirshov basis theory to differential difference algebras with respect to any left admissible ordering and develop the Groebner-Shirshov basis theory of finitely generated free modules over differential difference algebras. By using the theory we develop, we present an algorithm to compute the Gelfand-Kirillov dimensions of finitely generated modules over differential difference algebras. In Chapter 4, we first define skew solvable polynomial rings, which are generalizations of solvable polynomial algebras and (skew) PBW extensions. Then we present a signature-based algorithm for computing Groebner-Shirshov bases in skew solvable polynomial rings over fields. Our algorithm can detect redundant reductions and therefore it is more efficient than the traditional Buchberger algorithm. Finally, in Chapter 5, we summarize our results and propose possible future work.
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Books on the topic "Shirshova"

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G, Neĭman V., and Institut okeanologii im. P.P. Shirshova, eds. K istorii ėkspedit︠s︡ionnykh issledovaniĭ Instituta okeanologii im. P.P. Shirshova, 1946-2004. Moskva: Nauchnyĭ mir, 2005.

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Vinogradov, M. E., and S. S. Lappo. Polveka izuchenii︠a︡ Mirovogo okeana. Moskva: Nauka, 2000.

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Institut matematiki (Akademii͡a︡ nauk SSSR. Sibirskoe otdelenie), Altaĭskiĭ gosudarstvennyĭ universitet, and Moskovskiĭ gosudarstvennyĭ universitet im. M.V. Lomonosova., eds. Mezhdunarodnai͡a︡ konferent͡s︡ii͡a︡ po algebre: Posvi͡a︡shchennai͡a︡ pami͡a︡ti A.I. Shirshova (1921-1981), Barnaul, 20-25 avgusta 1991 g. Novosibirsk: In-t matematiki SO AN SSSR, 1991.

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Bokutʹ, L. A. (Leonid Arkadʹevich), 1937-, Bremner Murray R, and Kotchetov Mikhail V, eds. Selected works of A.I. Shirshov. Basel: Birkhäuser, 2009.

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Bokut, Leonid, Ivan Shestakov, Victor Latyshev, and Efim Zelmanov, eds. Selected Works of A.I. Shirshov. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8858-4.

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Malʹt︠s︡ev, I︠U︡ N., L. N. Petrova, and V. K. Krivolapova. Anatoliĭ Illarionovich Shirshov - iz kotory velikikh uchenykh. Aleĭsk: [Barnaul], 2003.

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International Conference on Algebra (2nd 1991 Barnaul, Altaĭskiĭ kraĭ, Russia). Second International Conference on Algebra: Dedicated to the memory of A.I. Shirshov : proceedings of the second International Conference on Algebra, August 20-25, 1991, Barnaul, Russua. Edited by Bokutʹ L. A. 1937-, Kostrikin A. I, and Kutateladze S. S. Providence, R.I: American Mathematical Society, 1995.

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Uchenye Instituta okeanologii im. P.P. Shirshova Rossiĭskoĭ Akademii Nauk (1946-2006). Moskva: In-tut okeanologii RAN, 2006.

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9

Bokut, Leonid, Yuqun Chen, and Kyriakos Kalorkoti. Grobner-Shirshov Bases: Normal Forms, Combinatorial and Decision Problems in Algebra. World Scientific Publishing Co Pte Ltd, 2018.

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Book chapters on the topic "Shirshova"

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Shirshov, A. I. "Subalgebras of Free Lie Algebras." In Selected Works of A.I. Shirshov, 3–13. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8858-4_1.

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Shirshov, A. I. "Some Problems in the Theory of Rings that are Nearly Associative." In Selected Works of A.I. Shirshov, 93–111. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8858-4_10.

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Shirshov, A. I. "On the Bases of a Free Lie Algebra." In Selected Works of A.I. Shirshov, 113–18. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8858-4_11.

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Shirshov, A. I. "Some Algorithmic Problems for ε-algebras." In Selected Works of A.I. Shirshov, 119–24. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8858-4_12.

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Shirshov, A. I. "Some Algorithmic Problems for Lie Algebras." In Selected Works of A.I. Shirshov, 125–30. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8858-4_13.

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Shirshov, A. I. "On a Hypothesis in the Theory of Lie Algebras." In Selected Works of A.I. Shirshov, 131–35. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8858-4_14.

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Shirshov, A. I. "On Some Groups which are Nearly Engel." In Selected Works of A.I. Shirshov, 137–47. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8858-4_15.

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Shirshov, A. I. "On Some Identical Relations for Algebras." In Selected Works of A.I. Shirshov, 149–52. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8858-4_16.

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Shirshov, A. I. "On Some Positively Definable Varieties of Groups." In Selected Works of A.I. Shirshov, 153–55. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8858-4_17.

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Shirshov, A. I. "On the Definition of the Binary-Lie Property." In Selected Works of A.I. Shirshov, 156–59. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8858-4_18.

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Conference papers on the topic "Shirshova"

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Bokut, L. A., Yuqun Chen, and Yu Li. "Gröbner-Shirshov Bases for Categories." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814365123_0001.

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Bokut, Leonid A. "The incipience of Gröbner–Shirshov bases." In 3rd International Congress in Algebras and Combinatorics (ICAC2017). WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811215476_0003.

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Bokut, L. A., and Yuqun Chen. "GRÖBNER-SHIRSHOV BASES: SOME NEW RESULTS." In Proceedings of the Second International Congress in Algebra and Combinatorics. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812790019_0003.

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BOKUT, L. A., Y. FONG, W. F. KE, and L. S. SHIAO. "GRÖBNER-SHIRSHOV BASES FOR THE BRAID SEMIGROUP." In Proceedings of the ICM Satellite Conference in Algebra and Related Topics. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705808_0005.

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Chen, Yuqun, and Lili Ni. "Gröbner-Shirshov bases for associative conformal modules." In 3rd International Congress in Algebras and Combinatorics (ICAC2017). WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811215476_0023.

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Bokut, L. A., Yuqun Chen, and K. P. Shum. "Some New Results on Gröbner-Shirshov Bases." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0005.

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Kolesnikov, P. "Gröbner–Shirshov bases for associative conformal algebras with arbitrary locality function." In 3rd International Congress in Algebras and Combinatorics (ICAC2017). WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811215476_0016.

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LEE, DENIS. "GRÖBNER—SHIRSHOV BASES AND NORMAL FORMS FOR THE COXETER GROUPS E6 AND E7." In Proceedings of the Second International Congress in Algebra and Combinatorics. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812790019_0016.

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Zatsepin, Andrey, Andrey Zatsepin, Sergey Kuklev, Sergey Kuklev, Alexander Ostrovskii, Alexander Ostrovskii, Vladimir Piotoukh, et al. "SHORT-TERM VARIABILITY OF COASTAL ZONE HYDRODYNAMICS UNDER AN EXTERNAL FORCING: OBSERVATIONS AT THE BLACK SEA RESEARCH SITE OF SIO RAS." In Managing risks to coastal regions and communities in a changing world. Academus Publishing, 2017. http://dx.doi.org/10.21610/conferencearticle_58b4315a048a4.

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Since 2010, the P.P. Shirshov Institute of Oceanology RAS (SIO RAS) in Gelendzhik maintains the research (observational) site for year round multi-disciplinary studies and monitoring of the marine environment in the coastal zone. Analysis of the data obtained at the observational site revealed the existence of well pronounced short-term variability of coastal zone hydrodynamics at time scales from 1-3 days to 1-2 weeks. The paper examines the role of external forcing (including the impact of adjoined open sea dynamics and wind stress) in the short-term variability of hydrodynamics and upper mixed layer evolution.
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Zatsepin, Andrey, Andrey Zatsepin, Sergey Kuklev, Sergey Kuklev, Alexander Ostrovskii, Alexander Ostrovskii, Vladimir Piotoukh, et al. "SHORT-TERM VARIABILITY OF COASTAL ZONE HYDRODYNAMICS UNDER AN EXTERNAL FORCING: OBSERVATIONS AT THE BLACK SEA RESEARCH SITE OF SIO RAS." In Managing risks to coastal regions and communities in a changing world. Academus Publishing, 2017. http://dx.doi.org/10.31519/conferencearticle_5b1b93915d1c11.31020337.

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Since 2010, the P.P. Shirshov Institute of Oceanology RAS (SIO RAS) in Gelendzhik maintains the research (observational) site for year round multi-disciplinary studies and monitoring of the marine environment in the coastal zone. Analysis of the data obtained at the observational site revealed the existence of well pronounced short-term variability of coastal zone hydrodynamics at time scales from 1-3 days to 1-2 weeks. The paper examines the role of external forcing (including the impact of adjoined open sea dynamics and wind stress) in the short-term variability of hydrodynamics and upper mixed layer evolution.
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