This article is cited in 6 papers

RESEARCH ARTICLE

On one class of algebras

Yuliia V. Zhuchok

Lugansk Taras Shevchenko National University

Abstract: In this paper a $g$-dimonoid which is isomorphic to the free $g$-dimonoid is given and a free $n$-nilpotent $g$-dimonoid is constructed. We also present the least $n$-nilpotent congruence on a free $g$-dimonoid and give numerous examples of $g$-dimonoids.

Keywords: dimonoid, $g$-dimonoid, free $g$-dimonoid, free $n$-nilpotent $g$-dimonoid, semigroup, congruence.

MSC: 08B20, 20M10, 20M50, 17A30, 17A32

Received: 10.11.2014
Revised: 12.01.2015

Language: English

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