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Algebra i logika, 2011, Volume 50, Number 4, Pages 471–496 (Mi al496)  
This article is cited in 27 scientific papers (total in 27 papers)

Dimonoids

A. V. Zhuchok

National Taras Shevchenko University of Kyiv, The Faculty of Mechanics and Mathematics, Kyiv, Ukraine
Full-text PDF (219 kB) Citations (27)
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Abstract: It is proved that a system of axioms for a dimonoid is independent and Cayley's theorem for semigroups has an analog in the class of dimonoids. A least separative congruence is constructed on an arbitrary dimonoid endowed with a commutative operation. It is shown that an appropriate quotient dimonoid is a commutative separative semigroup. A least separative congruence on a free commutative dimonoid is characterized. It is stated that each dimonoid with a commutative operation is a semilattice of Archimedean subdimonoids, each dimonoid with a commutative periodic semigroup is a semilattice of unipotent subdimonoids, and each dimonoid with a commutative operation is a semilattice of $a$-connected subdimonoids. Different dimonoid constructions are presented.
Keywords: dimonoid, dimonoid with commutative operation, free commutative dimonoid, semilattice of subdimonoids, semigroup.
Received: 20.08.2010
Revised: 25.11.2010
English version:
Algebra and Logic, 2011, Volume 50, Issue 4, Pages 323–340
DOI: https://doi.org/10.1007/s10469-011-9144-7
Bibliographic databases:
Document Type: Article
UDC: 512.57+512.579
Language: Russian
Citation: A. V. Zhuchok, “Dimonoids”, Algebra Logika, 50:4 (2011), 471–496; Algebra and Logic, 50:4 (2011), 323–340
Citation in format AMSBIB
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\by A.~V.~Zhuchok
\paper Dimonoids
\jour Algebra Logika
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\pages 471--496
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\transl
\jour Algebra and Logic
\yr 2011
\vol 50
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\pages 323--340
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    • This publication is cited in the following 27 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и логика Algebra and Logic
     
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