This article is cited in 12 papers

RESEARCH ARTICLE

Free $n$-nilpotent dimonoids

A. V. Zhuchok

Department of Mathematical Analysis and Algebra, Luhansk Taras Shevchenko National University, Oboronna str., 2, Luhansk, 91011, Ukraine

Abstract: We construct a free $n$-nilpotent dimonoid and describe its structure. We also characterize the least $n$-nilpotent congruence on a free dimonoid, construct a new class of dimonoids with zero and give examples of nilpotent dimonoids of nilpotency index $2$.

Keywords: $n$-nilpotent dimonoid, free $n$-nilpotent dimonoid, $0$-diband of subdimonoids, dimonoid, semigroup.

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

Received: 02.07.2013
Revised: 27.08.2013

Language: English

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