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Commutative Weakly Tripotent Group Rings
Authors: Peter V. Danchev
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Abstract
Very recently, Breaz and C\^{\i}mpean introduced and examined in Bull. Korean Math. Soc. (2018) the class of so-called {\it weakly tripotent rings} as those rings $R$ whose elements satisfy at leat one of the equations $x^3=x$ or $(1-x)^3=1-x$. These rings are generally non-commutative. We here obtain a criterion when the commutative group ring $RG$ is weakly tripotent in terms only of a ring $R$ and of a group $G$ plus their sections. \newline Actually, we also show that these weakly tripotent rings are {\it strongly invo-clean rings} in the sense of Danchev in Commun. Korean Math. Soc. (2017). Thereby, our established criterion somewhat strengthens previous results on commutative strongly invo-clean group rings, proved by the present author in Univ. J. Math. \& Math. Sci. (2018). Moreover, this criterion helps us to construct a commutative strongly invo-clean ring of characteristic $2$ which is {\it not} weakly tripotent, thus showing that these two ring classes are different.Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
”Acad. G. Bonchev”, str., bl. 8, 1113 Sofia
Bulgaria
E-mail: ,
Bulgarian Academy of Sciences
”Acad. G. Bonchev”, str., bl. 8, 1113 Sofia
Bulgaria
E-mail: ,
Fulltext
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Contents
- New Form of the Hidden Logarithm Problem and its Algebraic Support
- Inequalities of Hermite-Hadamard Type for K-Bounded Modulus Convex Complex Functions
- Commutative Weakly Tripotent Group Rings
- Isohedral tilings for hyperbolic translation group of genus two which admit additional isometries
- Interior angle sums of geodesic triangles in S2XR and H2XR geometries
- Signature Schemes on Algebras, Satisfying Enhanced Criterion of Post-quantum Security
- Quasi-Kählerian manifolds and quasi-Sasakian hypersurfaces axiom
- Laurent-Padé approximation for locating singularities of meromorphic functions with values given on simple closed contours
- Asymmetric Separation of Convex Sets
