Results 81 to 90 of about 39,950 (199)
Laser &Photonics Reviews, Volume 20, Issue 4, 19 February 2026.This manuscript demonstrates the improvements that single photon sources can gain if their source of excitation is quantum rather than classical. Illuminating a pair of identical two‐level systems, the author shows that the excitation with pulses of quantum light yields more antibunched and more indistinguishable emission than if the excitation were ...
Juan Camilo López Carreño
wiley +1 more source
The nilpotent regular element problem
, 2015 We use George Bergman's recent normal form for universally adjoining an inner inverse to show that, for general rings, a nilpotent regular element $x$ need not be unit-regular. This contrasts sharply with the situation for nilpotent regular elements in exchange rings (a large class of rings), and for general rings when all powers of the nilpotent ...
Ara, P., O'Meara, K. C.
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Strongly Invo. T- Clean Rings [PDF]
Al-Rafidain Journal of Computer Sciences and MathematicsIn this paper, we present the idea of a strongly invo. T-clean rings, which we define as rings with every a in R having the formula a = t + v, where t is a tripotent and v is an order two unit that commute.
Rand Alneamy, Nazar Shuker
doaj +1 more source
Direct sums of J-rings and radical rings
International Journal of Mathematics and Mathematical Sciences, 1995 Let R be a ring, J(R) the Jacobson radical of R and P the set of potent elements of R. We prove that if R satisfies (∗) given x, y in R there exist integers m=m(x,y)>1 and n=n(x,y)>1 such that xmy=xyn and if each x∈R is the sum of a potent element and a ...
Xiuzhan Guo
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On the girth of regular digraph of ideals of an Artinian ring
AKCE International Journal of Graphs and Combinatorics, 2015 Let R be a commutative ring. The regular digraph of ideals of R, denoted by Γ(R), is a digraph whose vertex-set is the set of all non-trivial ideals of R and, for every two distinct vertices I and J, there is an arc from I to J, whenever I contains an ...
Masoud Karimi
doaj +1 more source
The classification of modular Lie superalgebras of type M
Open Mathematics, 2015 The natural filtration of the infinite-dimensional simple modular Lie superalgebra M over a field of characteristic p > 2 is proved to be invariant under automorphisms by discussing ad-nilpotent elements.
Ma Lili, Chen Liangyun
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Finite groups whose order graph is C4-free [PDF]
Proceedings of the Estonian Academy of SciencesGiven a finite group G , the order graph of G, denoted by S(G), is a graph whose vertex set is G, and two distinct vertices a and b are adjacent if o(a) | o(b) or o(b) | o(a), where o(a), and o(b), are the orders of a and b in G, respectively.
Jin Chen, Jie Chen, Shixun Lin
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On connected components and perfect codes of proper order graphs of finite groups [PDF]
Proceedings of the Estonian Academy of SciencesLet G be a finite group with the identity element e. The proper order graph of G, denoted by â* (G), is an undirected graph with a vertex set G \ {e}, where two distinct vertices x and y are adjacent whenever o(x) | o(y) or o(y) | o(x), where o(x) and ...
Huani Li, Shixun Lin, Xuanlong Ma
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On Nilpotent Elements and Armendariz Modules
MathematicsFor a left module MR over a non-commutative ring R, the notion for the class of nilpotent elements (nilR(M)) was first introduced and studied by Sevviiri and Groenewald in 2014 (Commun. Algebra, 42, 571–577).
Nazeer Ansari +4 more
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On nilpotent elements of skew polynomial rings
Journal of Mathematical Extension, 2012 Summary: We study the structure of the set of nilpotent elements in skew polynomial ring \(R[x;\alpha]\), when \(R\) is an \(\alpha\)-Armendariz ring. We prove that if \(R\) is a nil \(\alpha\)-Armendariz ring and \(\alpha^t=I_R\), then the set of nilpotent elements of \(R\) is an \(\alpha\)-compatible subring of \(R\).
J. Esmaeili, E. Hashemi
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