Results 1 to 10 of about 355 (145)
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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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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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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Gradings induced by nilpotent elements
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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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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Математичні Студії, 2021 We investigate a few special decompositions in arbitrary rings and matrix rings over indecomposable rings into nilpotent and idempotent elements. Moreover, we also define and study the nilpotent sum trace number of nilpotent matrices over an arbitrary ...
P.V. Danchev
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Al-Rafidain Journal of Computer Sciences and Mathematics, 2009 In this paper we study idempotent elements, we give some new properties of idempotent elements and provide some exam we also study central idempotent elements and orthogonal idempotent elements and give some new properties of such idempotent ...
Nazar Shuker, Alaa Hammodat
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On the formal power series algebras generated by a vector space and a linear functional [PDF]
Journal of Hyperstructures, 2017 Let R be a vector space ( on C) and ϕ be an element of R∗ (the dual space of R), the product r · s = ϕ(r)s converts R into an associative algebra that we denote it by Rϕ.
A. R. Khoddami
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