This article is cited in 5 papers

RESEARCH ARTICLE

Free $(\ell r, rr)$-dibands

A. V. Zhuchok

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

Abstract: We prove that varieties of $(\ell r, rr)$-dibands and $(\ell n, rn)$-dibands coincide and describe the structure of free $(\ell r, rr)$-dibands. We also show that operations of an idempotent dimonoid with left (right) regular bands coincide, construct a new class of dimonoids and for such dimonoids give an example of a semiretraction.

Keywords: left (right) regular band, $(\ell r, rr)$-diband, diband of subdimonoids, dimonoid, semigroup.

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

Received: 03.03.2013
Revised: 03.04.2013

Language: English

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