Relevant bibliographies by topics / Nilpotentní ideál

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Academic literature on the topic 'Nilpotentní ideál'

Author: Grafiati
Published: 26 July 2021
Last updated: 10 February 2022

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Journal articles on the topic "Nilpotentní ideál"

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Marques-Smith, M. Paula O., and R. P. Sullivan. "The ideal structure of nilpotent-generated transformation semigroups." Bulletin of the Australian Mathematical Society 60, no. 2 (October 1999): 303–18. http://dx.doi.org/10.1017/s0004972700036418.

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In 1987 Sullivan determined the elements of the semigroup N(X) generated by all nilpotent partial transformations of an infinite set X; and later in 1997 he studied subsemigroups of N(X) defined by restricting the index of the nilpotents and the cardinality of the set. Here, we describe the ideals and Green's relations on such semigroups, like Reynolds and Sullivan did in 1985 for the semigroup generated by all idempotent total transformations of X. We then use this information to describe the congruences on certain Rees factor semigroups and to construct families of congruence-free semigroups with interesting algebraic properties. We also study analogous questions for X finite and for one-to-one partial transformations.
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Yaqub, Adil. "Weakly periodic-like rings and commutativity." Studia Scientiarum Mathematicarum Hungarica 43, no. 3 (September 1, 2006): 275–84. http://dx.doi.org/10.1556/sscmath.43.2006.3.1.

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A ring R is called periodic if, for every x in R, there exist distinct positive integers m and n such that xm=xn. An element x is called potent if xk=x for some integer k≯1. A ring R is called weakly periodic if every x in R can bewritten in the form x=a+b for some nilpotent element a and some potent element b. A ring R is called weakly periodic-like if every x in R which is not in the center of R can be written in the form x=a+b, where a is nilpotent and b is potent. Our objective is to study the structure of weakly periodic-like rings, with particular emphasis on conditions which yield such rings commutative, or conditions which render the nilpotents N as an ideal of R and R/N as commutative.
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Abu-Khuzam, Hazar, and Adil Yaqub. "Structure of Certain Periodic Rings." Canadian Mathematical Bulletin 28, no. 1 (March 1, 1985): 120–23. http://dx.doi.org/10.4153/cmb-1985-014-9.

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AbstractLet R be a periodic ring, N the set of nilpotents, and D the set of right zero divisors of R. Suppose that (i) N is commutative, and (ii) every x in R can be uniquely written in the form x = e + a, where e2 = e and a ∊ N. Then N is an ideal in R and R/N is a Boolean ring. If (i) is satisfied but (ii) is now assumed to hold merely for those elements x ∊ D, and if 1 ∊ R, then N is still an ideal in R and R/N is a subdirect sum of fields. It is further shown that if (i) is satisfied but (ii) is replaced by: "every right zero divisor is either nilpotent or idempotent," and if 1 ∊ R, then N is still an ideal in R and R/N is either a Boolean ring or a field.
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Mohammadzadeh, E., G. Muhiuddin, J. Zhan, and R. A. Borzooei. "Nilpotent fuzzy lie ideals." Journal of Intelligent & Fuzzy Systems 39, no. 3 (October 7, 2020): 4071–79. http://dx.doi.org/10.3233/jifs-200211.

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In this paper, we introduce a new definition for nilpotent fuzzy Lie ideal, which is a well-defined extension of nilpotent Lie ideal in Lie algebras, and we name it a good nilpotent fuzzy Lie ideal. Then we prove that a Lie algebra is nilpotent if and only if any fuzzy Lie ideal of it, is a good nilpotent fuzzy Lie ideal. In particular, we construct a nilpotent Lie algebra via a good nilpotent fuzzy Lie ideal. Also, we prove that with some conditions, every good nilpotent fuzzy Lie ideal is finite. Finally, we define an Engel fuzzy Lie ideal, and we show that every Engel fuzzy Lie ideal of a finite Lie algebra is a good nilpotent fuzzy Lie ideal. We think that these notions could be useful to solve some problems of Lie algebras with nilpotent fuzzy Lie ideals.
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Woods, William. "On the structure of virtually nilpotent compact p-adic analytic groups." Journal of Group Theory 21, no. 1 (January 1, 2018): 165–88. http://dx.doi.org/10.1515/jgth-2017-0017.

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AbstractLetGbe a compactp-adic analytic group. We recall the well-understood finite radical{\Delta^{+}}and FC-centre Δ, and introduce ap-adic analogue of Roseblade’s subgroup{\mathrm{nio}(G)}, the unique largest orbitally sound open normal subgroup ofG. Further, whenGis nilpotent-by-finite, we introduce the finite-by-(nilpotentp-valuable) radical{\mathbf{FN}_{p}(G)}, an open characteristic subgroup ofGcontained in{\mathrm{nio}(G)}. By relating the already well-known theory of isolators with Lazard’s notion ofp-saturations, we introduce the isolated lower central (resp. isolated derived) series of a nilpotent (resp. soluble)p-valuable group, and use this to study the conjugation action of{\mathrm{nio}(G)}on{\mathbf{FN}_{p}(G)}. We emerge with a structure theorem forG,1\leq\Delta^{+}\leq\Delta\leq\mathbf{FN}_{p}(G)\leq\mathrm{nio}(G)\leq G,in which the various quotients of this series of groups are well understood. This sheds light on the ideal structure of the Iwasawa algebras (i.e. the completed group ringskG) of such groups, and will be used in future work to study the prime ideals of these rings.
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PANYUSHEV, DMITRI I., and OKSANA S. YAKIMOVA. "NILPOTENT SUBSPACES AND NILPOTENT ORBITS." Journal of the Australian Mathematical Society 106, no. 1 (May 30, 2018): 104–26. http://dx.doi.org/10.1017/s1446788718000071.

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Let $G$ be a semisimple complex algebraic group with Lie algebra $\mathfrak{g}$. For a nilpotent $G$-orbit ${\mathcal{O}}\subset \mathfrak{g}$, let $d_{{\mathcal{O}}}$ denote the maximal dimension of a subspace $V\subset \mathfrak{g}$ that is contained in the closure of ${\mathcal{O}}$. In this note, we prove that $d_{{\mathcal{O}}}\leq {\textstyle \frac{1}{2}}\dim {\mathcal{O}}$ and this upper bound is attained if and only if ${\mathcal{O}}$ is a Richardson orbit. Furthermore, if $V$ is $B$-stable and $\dim V={\textstyle \frac{1}{2}}\dim {\mathcal{O}}$, then $V$ is the nilradical of a polarisation of ${\mathcal{O}}$. Every nilpotent orbit closure has a distinguished $B$-stable subspace constructed via an $\mathfrak{sl}_{2}$-triple, which is called the Dynkin ideal. We then characterise the nilpotent orbits ${\mathcal{O}}$ such that the Dynkin ideal (1) has the minimal dimension among all $B$-stable subspaces $\mathfrak{c}$ such that $\mathfrak{c}\cap {\mathcal{O}}$ is dense in $\mathfrak{c}$, or (2) is the only $B$-stable subspace $\mathfrak{c}$ such that $\mathfrak{c}\cap {\mathcal{O}}$ is dense in $\mathfrak{c}$.
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Eslami, Esfandiar, and Patrick Stewart. "Two-sided essential nilpotence." International Journal of Mathematics and Mathematical Sciences 15, no. 2 (1992): 351–54. http://dx.doi.org/10.1155/s0161171292000449.

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An idealIof a ringAis essentially nilpotent ifIcontains a nilpotent idealNofAsuch thatJ⋂N≠0wheneverJis a nonzero ideal ofAcontained inI. We show that each ringAhas a unique largest essentially nilpotent idealEN(A). We study the properties ofEN(A)and, in particular, we investigate how this ideal behaves with respect to related rings.
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JESPERS, E., and M. H. SHAHZAMANIAN. "A DESCRIPTION OF A CLASS OF FINITE SEMIGROUPS THAT ARE NEAR TO BEING MAL'CEV NILPOTENT." Journal of Algebra and Its Applications 12, no. 05 (May 7, 2013): 1250221. http://dx.doi.org/10.1142/s0219498812502210.

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In this paper we continue the investigation on the algebraic structure of a finite semigroup S that is determined by its associated upper non-nilpotent graph [Formula: see text]. The vertices of this graph are the elements of S and two vertices are adjacent if they generate a semigroup that is not nilpotent (in the sense of Mal'cev). We introduce a class of semigroups in which the Mal'cev nilpotent property lifts through ideal chains. We call this the class of pseudo-nilpotent semigroups. The definition is such that the global information that a semigroup is not nilpotent induces local information, i.e. some two-generated subsemigroups are not nilpotent. It turns out that a finite monoid (in particular, a finite group) is pseudo-nilpotent if and only if it is nilpotent. Our main result is a description of pseudo-nilpotent finite semigroups S in terms of their associated graph [Formula: see text]. In particular, S has a largest nilpotent ideal, say K, and S/K is a 0-disjoint union of its connected components (adjoined with a zero) with at least two elements.
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Röhl, Frank. "A Remark on the Loewy-Series of Certain Hopf Algebras." Canadian Mathematical Bulletin 32, no. 2 (June 1, 1989): 190–93. http://dx.doi.org/10.4153/cmb-1989-028-6.

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AbstractAn easy proof will be given to show that for finite dimensional Hopf-algebras with nilpotent augmentation ideal over the field of p elements, the upper and lower Loewy-series coincide. In particular, this holds for the restricted universal envelope of nilpotent Lie-p-algebras with nilpotent p-map.
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Artemovych, Orest D. "Associative rings in which nilpotents form an ideal." Studia Scientiarum Mathematicarum Hungarica 56, no. 2 (June 2019): 177–84. http://dx.doi.org/10.1556/012.2019.56.2.1428.

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Abstract It is shown that if N(R) is a Lie ideal of R (respectively Jordan ideal and R is 2-torsion-free), then N(R) is an ideal. Also, it is presented a characterization of Noetherian NR rings with central idempotents (respectively with the commutative set of nilpotent elements, the Abelian unit group, the commutative commutator set).
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Dissertations / Theses on the topic "Nilpotentní ideál"

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Talley, Amanda Renee. "An Introduction to Lie Algebra." CSUSB ScholarWorks, 2017. https://scholarworks.lib.csusb.edu/etd/591.

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An (associative) algebra is a vector space over a field equipped with an associative, bilinear multiplication. By use of a new bilinear operation, any associative algebra morphs into a nonassociative abstract Lie algebra, where the new product in terms of the given associative product, is the commutator. The crux of this paper is to investigate the commutator as it pertains to the general linear group and its subalgebras. This forces us to examine properties of ring theory under the lens of linear algebra, as we determine subalgebras, ideals, and solvability as decomposed into an extension of abelian ideals, and nilpotency, as decomposed into the lower central series and eventual zero subspace. The map sending the Lie algebra L to a derivation of L is called the adjoint representation, where a given Lie algebra is nilpotent if and only if the adjoint is nilpotent. Our goal is to prove Engel's Theorem, which states that if all elements of L are ad-nilpotent, then L is nilpotent.
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Procházková, Zuzana. "Význačné prvky grupových okruhů." Master's thesis, 2021. http://www.nusl.cz/ntk/nusl-448402.

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Title: Distinguished elements of group rings Author: Bc. Zuzana Procházková Department: Department of Algebra Supervisor: doc. Mgr. et Mgr. Jan Žemlička, Ph.D., Department of Algebra Abstract: This thesis is about finding idempotents in a group ring. We describe three techniques of finding idempotents in a semisimple group ring and in the last chapter there is an attempt to find idempotents in a group ring that does not have to be semisimple. The first technique uses representations and characters of a group. The second technique finds idempotents through the use of Shoda pairs. The third technique lifts idempotent from the factor ring with the help of CNC system of ideals, which is a generalization of a well-known technique with nilpotent ideals, and it is here extended to group rings formed by non-abelian group and noncommutative ring. iii
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Books on the topic "Nilpotentní ideál"

1

Borho, W. Nilpotent orbits, primitive ideals, and characteristic classes: A geometric perspective in ring theory. Boston: Birkhäuser, 1989.

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