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Journal of Mathematics, 2014 The concept of nil-symmetric rings has been introduced as a generalization of symmetric rings and a particular case of nil-semicommutative rings. A ring R is called right (left) nil-symmetric if, for a,b,c∈R, where a,b are nilpotent elements, abc=0 (cab=
Uday Shankar Chakraborty, Krishnendu Das
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Symmetrization in Clean and Nil-Clean Rings [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2020 We introduce and investigate D-clean and D-nil-clean rings as well as some other closely related symmetric versions of cleanness and nil-cleanness. A comprehensive structural characterization is given for these symmetrically clean and symmetrically nil ...
Danchev, Peter Vasilevich
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Commutativity of Prime Rings with Symmetric Biderivations
Discussiones Mathematicae - General Algebra and Applications, 2018 The present paper shows some results on the commutativity of R: Let R be a prime ring and for any nonzero ideal I of R, if R admits a biderivation B such that it satisfies any one of the following properties (i) B([x, y], z) = [x, y], (ii) B([x, y], m) +
Reddy B. Ramoorthy, Reddy C. Jaya Subba
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Basic examples and extensions of symmetric rings
Journal of Pure and Applied Algebra, 2005 A ring \(R\) with identity is called `symmetric' if \(rst=0\) implies \(rts=0\) for all \(r,s,t\in R\). The authors discuss basic examples and extensions, and prove that a minimal noncommutative symmetric ring is of order 16 and is unique up to isomorphism. This ring is given in Example 2.5.
Yang Lee, Chan Huh, Hong Kee Kim
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On duo, reversible and symmetric group rings
Sao Paulo Journal of Mathematical SciencesLet $RG$ denote the group ring of the torsion group $G$ over a commutative ring $R$ with identity. In this paper we present proofs of some statements that appear without to be proved in the literature. We establish the valid implications between the ring-theoretic conditions duo, reversible, SI property and symmetric in the setting of group rings.
John H Castillo +2 more
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On Ideals in Partially Ordered Ternary Semigroups
Ratio Mathematica, 2023 The concept of ideals has been extensively studied through various algebraic structures such as near-rings, involution rings, regular rings, gamma-rings, semigroups, ordered semigroups, ternary semigroups and ordered ternary semigroups.
Dattatray Nabajirao Shinde +1 more
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Ring-originated anisotropy of local structural ordering in amorphous and crystalline silicon dioxide
Communications Materials, 2023 Rings comprising chemically bonded atoms are essential topological motifs for the structural ordering of network-forming materials. Quantification of such larger motifs beyond short-range pair correlation is essential for understanding the linkages ...
Motoki Shiga +3 more
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Orthogonal Semiderivations and Symmetric Bi-semiderivations in Semiprime Rings
Cumhuriyet Science Journal, 2022 In this paper, orthogonality for symmetric bi-semiderivations is defined and some results are obtained when two symmetric bi-semiderivations are orthogonal.
Damla Yılmaz
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On Zero-Symmetric Left Centrally Prime Near-Rings [PDF]
Kirkuk Journal of Science, 2007 Our aim in this paper is: to give some properties of zero-symmetric left centrally prime near-rings, then looking for those conditions which make zero-symmetric left centrally prime near-rings abelian, so that several conditions are given under which ...
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When are the natural embeddings of classical invariant rings pure?
Forum of Mathematics, Sigma, 2023 Consider a reductive linear algebraic group G acting linearly on a polynomial ring S over an infinite field; key examples are the general linear group, the symplectic group, the orthogonal group, and the special linear group, with the classical ...
Melvin Hochster +3 more
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