Results 11 to 20 of about 2,773,140 (200)
Nilpotent Elements of Residuated Lattices [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 Some properties of the nilpotent elements of a residuated lattice are studied. The concept of cyclic residuated lattices is introduced, and some related results are obtained.
Shokoofeh Ghorbani, Lida Torkzadeh
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Annihilators of nilpotent elements [PDF]
International Journal of Mathematics and Mathematical Sciences, 2005 Let x be a nilpotent element of an infinite ring R (not necessarily with 1). We prove that A(x)—the two-sided annihilator of x—has a large intersection with any infinite ideal I of R in the sense that card(A(x)∩I)=cardI.
Abraham A. Klein
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On Nilpotent Elements of Skew Polynomial Rings
Journal of Mathematical Extension, 2012 We study the structure of the set of nilpotent elements in skew polynomial ring R[x; α], when R is an α-Armendariz ring. We prove that if R is a nil α-Armendariz ring and α t = IR, then the set of nilpotent elements of R is an α-compatible subrng of ...
J. Esmaeili, E. Hashemi
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Eurasian Journal of Science and Engineering, 2017 In this paper we study semi nilpotent elements in rings. It is shown that every element of Z nwhere n is square free is a trivial semi nilpotent. It is proved that every nontrivial nilpotent element is a nontrivial semi nilpotent.
Kurdistan M. Ali , Parween A. Hummadi
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Gradings induced by nilpotent elements [PDF]
Linear Algebra and its Applications, 2023 An element a is nilpotent last-regular if it is nilpotent and its last nonzero power is von Neumann regular. In this paper we show that any nilpotent last-regular element a in an associative algebra R over a ring of scalars Φ gives rise to a complete system of orthogonal idempotents that induces a finite Z-grading on R; we also show that such element ...
Esther García +3 more
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Fully commutative elements and spherical nilpotent orbits [PDF]
Journal of Algebra, 2022 Let g be a simple Lie algebra, with fixed Borel subalgebra b and with Weyl group W. Expanding on previous work of Fan and Stembridge in the simply laced case, this note aims to study the fully commutative elements of W, and their connections with the ...
Jacopo Gandini
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Strongly Ad-Nilpotent Elements of the Lie Algebra of Upper Triangular Matrices
Journal of Mathematics, 2022 In this paper, the strongly ad-nilpotent elements of the Lie algebra tn,ℂ of upper triangular complex matrices are studied. We prove that all the nilpotent matrices in tn,ℂ are strongly ad-nilpotent if and only if n≤6. Additionally, we prove that all the
Zhiguang Hu
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Theory and Applications of Graphs, 2021 In this article, we introduce the concept of nilpotent graph of a finite commutative ring. The set of all non nilpotent elements of a ring is taken as the vertex set and two vertices are adjacent if and only if their sum is nilpotent.
Dhiren Basnet, Ajay Sharma, Rahul Dutta
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Nilpotent elements and Armendariz rings
Journal of Algebra, 2008 Let \(R\) denote an associative ring with \(1\), and let \(\text{nil}(R)\) denote the set of nilpotent elements. Further, let \(f(x)=\sum_{i=0}^ma_ix^i,g(x)=\sum_{j=0}^nb_jx^j\in R[x]\) denote two arbitrary polynomials. One says that \(R\) is an Armendariz ring if \(f(x)g(x)=0\) implies that \(a_ib_j=0\) for all \(i\) and \(j\).
Ramon Antoine
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Unit-Regularity of Regular Nilpotent Elements [PDF]
Algebras and Representation Theory, 2016 In the revision some typos are corrected, minor modifications are made and also references to two related papers are added.
Dinesh Khurana
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