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Research Paper | Mathematics | India | Volume 9 Issue 1, January 2020

A Mathematics Letter Lecture Note on Some Variety of Algebraic Γ-Structures

Abul Basar

Abstract: Algebraic -structures represent a natural generalization of classical algebraic struc- tures. Results studied in semigroups are particular cases of those studied in -semigroups as every semigroup is a -semigroups but not vice-versa. This research paper is based on the introduction and initiation of rectangular -semigroups, quasi-rectangular -semigroups, total -semigroups, viable -semigroups and idempotent -semigroups. Among lots of results, we prove that a rect- angular -semigroup is the direct product of a left singular and a right singular -semigroups. Moreover, this product is unique up to isomorphism.

Keywords: semigroup, rectangular bands, rectangular semigroup, total semigroup, viable semigroup, quasi-rectangular -semigroup, singular semigroup, ideal

Edition: Volume 9 Issue 1, January 2020,

Pages: 113 - 117

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