Results 51 to 60 of about 60,182 (167)
Al-Rafidain Journal of Computer Sciences and MathematicsAn element is considered as a strongly SITN, if it is the sum of idempotent, tripotent and a nilpotent, that commute with one another. A ring R is referred to be SITN ring if each member of R is a strongly SITN.
Rafal Dhanoon, Nazar Shuker
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The strong nil-cleanness of semigroup rings
Open Mathematics, 2020 In this paper, we study the strong nil-cleanness of certain classes of semigroup rings. For a completely 0-simple semigroup M=ℳ0(G;I,Λ;P)M={ {\mathcal M} }^{0}(G;I,\text{Λ};P), we show that the contracted semigroup ring R0[M]{R}_{0}{[}M] is ...
Ji Yingdan
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ON CLEAN LAURENT SERIES RINGS [PDF]
Journal of the Australian Mathematical Society, 2013 AbstractHere we prove that, for a $2$-primal ring $R$, the Laurent series ring $R((x))$ is a clean ring if and only if $R$ is a semiregular ring with $J(R)$ nil. This disproves the claim in K. I. Sonin [‘Semiprime and semiperfect rings of Laurent series’, Math. Notes 60 (1996), 222–226] that the Laurent series ring over a clean ring is again clean.
Zhou, Yiqiang, Ziembowski, Michał
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On Weakly 2-Invo Clean Rings With Some Properties in Graph Theory
International Journal of Mathematics and Mathematical SciencesThe concept of a weakly two-involution clean ring is presented; it is a generalization of two-involution clean ring, which allows the addition of more elements to a ring, which will be observed in its graph theoretic representation.
Salim Ghadeer Salim +2 more
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Symmetrization in Clean and Nil-Clean Rings
Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics, 2020 A ring \(R\) is said to be \textsl{double nil-clean} or just \textsl{ D-nil-clean} for short if, for every \(a\in R\), there exists \(e\in (aRa)\cap Id(R)\) such that \(a=e+q\) for some \(q\in \mathrm{Nil}(R)\). Similarly, a ring \(R\) is said to be \textsl{double clean} or just \textsl{D-clean} for short if, for each \(a\in R\), there exists \(e\in ...
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Nil Clean Graphs of Rings [PDF]
Algebra Colloquium, 2017 In this article, we define the nil clean graph of a ring R. The vertex set is the ring R, and two ring elements a and b are adjacent if and only if a + b is nil clean in R. Graph theoretic properties like the girth, dominating sets, diameter, etc., of the nil clean graph are studied for finite commutative rings.
Basnet, Dhiren Kumar +1 more
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Conditions when abelian clean Bezout ring is an elementary divisors ring (in Ukrainian) [PDF]
Математичні Студії, 2012 In the paper it is proved that the abelian clean Bezout ring is an elementary divisors ring, if and only if it is a duo-ring and shows that the projective-free right (left) Bezout ring is right (left) Hermite ring if his stable rank not more 2.
I. S. Vasyunyk
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Some properties of skew Hurwitz series
Le Matematiche, 2014 In this paper we show that, if R is a ring and σ an endomorphism of R, then the skew Hurwitz series ring T = (HR, σ ) is an n-clean ring if and only if R is an n-clean ring.
A. M. Hassanein, Mohamed A. Farahat
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Beilstein Journal of Organic Chemistry, 2013 Coarctate reactions are defined as reactions that include atoms at which two bonds are made and two bonds are broken simultaneously. In the pursuit of the discovery of new coarctate reactions we investigate the fragmentation reactions of cyclic ketals ...
Götz Bucher +2 more
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Tripotents: a class of strongly clean elements in rings
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018 Periodic elements in a ring generate special classes of strongly clean elements. In particular, elements b such that b = b3+, which are called tripotents and include idempotents, negative of idempotents and order 2 units, are strongly clean.
Călugăreanu Grigore
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