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n-Torsion Regular Rings
Authors: P. V. Danchev
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Abstract
As proper subclasses of the classes of unit-regular and strongly regular rings, respectively, the two new classes of $n$-torsion regular rings and strongly $n$-torsion regular rings are introduced and investigated for any natural number $n$. Their complete isomorphism classification is given as well. More concretely, although it has been recently shown by Nielsen-\v{S}ter (TAMS, 2018) that unit-regular rings need not be strongly clean, the rather curious fact that, for each positive odd integer $n$, the $n$-torsion regular rings are always strongly clean is proved.Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences,
1113 Sofia, Bulgaria
E-mail: ,
Bulgarian Academy of Sciences,
1113 Sofia, Bulgaria
E-mail: ,
Fulltext
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Contents
- Finite 2-groups with a non-Dedekind non-metacyclic norm of Abelian non-cyclic subgroups
- n-Torsion Regular Rings
- On invariant submanifolds of S-manifolds
- On fully idempotent semimodules
- On generalization of the notion of Moufang loop to n-ary case
- Finite Non-commutative Associative Algebras for Setting the Hidden Discrete Logarithm Problem and Post-quantum Cryptoschemes on its Base
- On the number of topologies on countable fields
- Isohedral tilings by 14-, 16- and 18-gons for hyperbolic translation group of genus two
- A note on almost contact metric 2- and 3-hypersurfaces in W_4-manifolds
- Morita contexts and closure operators in modules
- Examples of bipartite graphs which are not cyclically-interval colorable
- Academician Vladimir Arnautov 80th anniversary
