On quasi-Frobenius semigroup algebras
B. V. Novikov
TL;DR
This paper introduces quasi-Frobenius semigroups and establishes precise conditions for their semigroup algebras to possess the quasi-Frobenius property, advancing understanding in algebraic structures.
Contribution
It defines quasi-Frobenius semigroups and provides necessary and sufficient conditions for their semigroup algebras to be quasi-Frobenius, a novel characterization in algebra.
Findings
Characterization of quasi-Frobenius semigroups
Necessary and sufficient conditions for semigroup algebra to be quasi-Frobenius
Extension of algebraic theory to 0-cancellative semigroups
Abstract
We define quasi-Frobenius semigroups and find necessary and sufficient conditions under which a semigroup algebra of a 0-cancellative semigroup is quasi-Frobenius.
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Taxonomy
TopicsRings, Modules, and Algebras · Fuzzy and Soft Set Theory · Advanced Topics in Algebra