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Relevant bibliographies by topics / Diamond lemma

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Journal articles
Dissertations / Theses
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Academic literature on the topic 'Diamond lemma'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Diamond lemma"

1

Chen, Yuqun, Yongshan Chen, and Chanyan Zhong. "Composition-diamond lemma for modules." Czechoslovak Mathematical Journal 60, no. 1 (2010): 59–76. http://dx.doi.org/10.1007/s10587-010-0018-2.

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Zhang, Guangliang, and Yuqun Chen. "A New Composition-Diamond Lemma for Dialgebras." Algebra Colloquium 24, no. 02 (2017): 323–50. http://dx.doi.org/10.1142/s1005386717000207.

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Bokut, Chen and Liu in 2010 gave a Composition-Diamond lemma for dialgebras. In this paper, by introducing an arbitrary monomial-center ordering, we give a new Composition-Diamond lemma for dialgebras which makes the two conditions in Bokut, Chen and Liu’s result equivalent. The new lemma is more useful and convenient than the one Bokut, Chen and Liu got. We show that every ideal of the free dialgebra generated by a set X has a unique reduced Gröbner-Shirshov basis. As applications, we give a method to find normal forms of elements of an arbitrary disemigroup, in particular, two Zhuchoks’ norm

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Bokut, L. A., Y. Fong, and W. F. Ke. "Composition-Diamond Lemma for associative conformal algebras." Journal of Algebra 272, no. 2 (2004): 739–74. http://dx.doi.org/10.1016/s0021-8693(03)00341-7.

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BALODI, MAMTA, HUA-LIN HUANG, and SHIV DATT KUMAR. "Diamond lemma for the group graded quasi-algebras." Proceedings - Mathematical Sciences 126, no. 3 (2016): 341–52. http://dx.doi.org/10.1007/s12044-016-0292-5.

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Ni, Lili, and Yuqun Chen. "A new Composition-Diamond lemma for associative conformal algebras." Journal of Algebra and Its Applications 16, no. 05 (2017): 1750094. http://dx.doi.org/10.1142/s0219498817500943.

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Let [Formula: see text] be the free associative conformal algebra generated by a set [Formula: see text] with a bounded locality [Formula: see text]. Let [Formula: see text] be a subset of [Formula: see text]. A Composition-Diamond lemma for associative conformal algebras is first established by Bokut, Fong and Ke in 2004 [L. A. Bokut, Y. Fong and W.-F. Ke, Composition-Diamond Lemma for associative conformal algebras, J. Algebra 272 (2004) 739–774] which claims that if (i) [Formula: see text] is a Gröbner–Shirshov basis in [Formula: see text], then (ii) the set of [Formula: see text]-irreducib

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Bokut, L. A., Yuqun Chen, and Yongshan Chen. "Composition–Diamond lemma for tensor product of free algebras." Journal of Algebra 323, no. 9 (2010): 2520–37. http://dx.doi.org/10.1016/j.jalgebra.2010.02.021.

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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 (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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Tuniyaz, Rabigul, and Abdukadir Obul. "Gröbner–Shirshov basis method for multiple tensor products of some associative algebras." Asian-European Journal of Mathematics 12, no. 01 (2019): 1950015. http://dx.doi.org/10.1142/s1793557119500153.

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In this paper, we establish Composition-Diamond lemma for multiple tensor products of commutative algebra [Formula: see text], free associative algebras [Formula: see text], Grassman algebras [Formula: see text] and path algebras [Formula: see text] over a field [Formula: see text].

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Zhang, Meili, and Bo Deng. "Prime Decomposition of Three-Dimensional Manifolds into Boundary Connected Sum." ISRN Applied Mathematics 2014 (February 19, 2014): 1–3. http://dx.doi.org/10.1155/2014/717265.

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In 2003 Matveev suggested a new version of the Diamond Lemma suitable for topological applications. We apply this result to different situations and get a new conceptual proof of theorem on decomposition of three-dimensional manifolds into boundary connected sum of prime components.

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QIU, JIANJUN, та YUQUN CHEN. "COMPOSITION-DIAMOND LEMMA FOR λ-DIFFERENTIAL ASSOCIATIVE ALGEBRAS WITH MULTIPLE OPERATORS". Journal of Algebra and Its Applications 09, № 02 (2010): 223–39. http://dx.doi.org/10.1142/s0219498810003859.

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In this paper, we establish the Composition-Diamond lemma for λ-differential associative algebras over a field K with multiple operators. As applications, we obtain Gröbner–Shirshov bases of free λ-differential Rota–Baxter algebras. In particular, linear bases of free λ-differential Rota–Baxter algebras are obtained and consequently, the free λ-differential Rota–Baxter algebras are constructed by words.

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Dissertations / Theses on the topic "Diamond lemma"

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Hellström, Lars. "The Diamond Lemma for Power Series Algebras." Doctoral thesis, Umeå University, Mathematics and Mathematical Statistics, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-92.

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<p>The main result in this thesis is the generalisation of Bergman's diamond lemma for ring theory to power series rings. This generalisation makes it possible to treat problems in which there arise infinite descending chains. Several results in the literature are shown to be special cases of this diamond lemma and examples are given of interesting problems which could not previously be treated. One of these examples provides a general construction of a normed skew field in which a custom commutation relation holds.</p><p>There is also a general result on the structure of totally ordered semig

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Ge, Wenfeng. "Gröbner Bases Theory and The Diamond Lemma." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2951.

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Commutative Gröbner bases theory is well known and widely used. In this thesis, we will discuss thoroughly its generalization to noncommutative polynomial ring <em>k</em><<em>X</em>> which is also an associative free algebra. We introduce some results on monomial orders due to John Lawrence and the author. We show that a noncommutative monomial order is a well order while a one-sided noncommutative monomial order may not be. Then we discuss the generalization of polynomial reductions, S-polynomials and the characterizations of noncommutative Gröbner bases. Some results due to Mora

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Ronchetti, Niccolò. "Il Diamond lemma e il teorema di Poincaré-Birkhoff-Witt sugli anelli." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amslaurea.unibo.it/1185/.

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Holm, Christoffer. "A Noncommutative Catenoid." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-139794.

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Noncommutative geometry generalizes many geometric results from such ﬁelds as diﬀerential geometry and algebraic geometry to a context where commutativity cannot be assumed. Unfortunately there are few concrete non-trivial examples of noncommutative objects. The aim of this thesis is to construct a noncommutative surface <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmathcal%7BC%7D_%5Chbar" /> which will be a generalization of the well known surface called the catenoid. This surface will be constructed using the Diamond lemma, derivations will be constructed over <img src="http://

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Book chapters on the topic "Diamond lemma"

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Brown, Ken A., and Ken R. Goodearl. "The Diamond Lemma." In Lectures on Algebraic Quantum Groups. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8205-7_11.

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Scholze, Peter, and Jared Weinstein. "Drinfeld’s lemma for diamonds." In Berkeley Lectures on p-adic Geometry. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691202082.003.0016.

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This chapter addresses Drinfeld's lemma for diamonds. It proves a local analogue of Drinfeld's lemma, thereby giving a first nontrivial argument involving diamonds. This lecture is entirely about fundamental groups. A diamond is defined to be connected if it is not the disjoint union of two open subsheaves. For a connected diamond, finite étale covers form a Galois category. As such, for a geometric point, one can define a profinite group, such that finite sets are equivalent to finite étale covers. In this proof, the chapter uses the formalism of diamonds rather heavily to transport finite étale maps between different presentations of a diamond as the diamond of an analytic adic space.

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"Composition-Diamond Lemma." In Gröbner–Shirshov Bases. WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789814619493_0003.

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"The Diamond Lemma." In A Tour of Representation Theory. American Mathematical Society, 2018. http://dx.doi.org/10.1090/gsm/193/16.

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"Drinfeld’s lemma for diamonds." In Berkeley Lectures on p-adic Geometry. Princeton University Press, 2020. http://dx.doi.org/10.2307/j.ctvs32rc9.19.

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"Lecture 16. Drinfeld's lemma for diamonds." In Berkeley Lectures on p-adic Geometry. Princeton University Press, 2020. http://dx.doi.org/10.1515/9780691202150-017.

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