I. B. Kozhukhov, A. R. Haliullina, “A characterization of subdirectly irreducible acts”, Prikl. Diskr. Mat., 2015, no. 1(27), 5

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Prikladnaya Diskretnaya Matematika, 2015, Number 1(27), Pages 5–16 (Mi pdm491)

This article is cited in 8 scientific papers (total in 8 papers)

Theoretical Foundations of Applied Discrete Mathematics

A characterization of subdirectly irreducible acts

I. B. Kozhukhov, A. R. Haliullina

National Research University of Electronic Technology, Moscow, Russia

Full-text PDF (623 kB) Citations (8)

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Abstract: The subdirectly irreducible acts (automata) over semigroups are investigated. In 1974, E. N. Roiz proved that such acts have at most two zeros. Here, we characterize subdirectly irreducible acts with two zeros and reduce the characterization of an act with one zero or without zeros to the structure of its least non-trivial subact. We fully characterize the subdirectly irreducible acts over rectangular bands. As the corollaries we have a characterization of subdirectly irreducible acts over right zero semigroups and the Moghaddassi's result about acts over left zero semigroups.

Keywords: act over semigroup, subdirectly irreducible act, rectangular band.

Bibliographic databases:

Document Type: Article

UDC: 512.579

Language: Russian

Citation: I. B. Kozhukhov, A. R. Haliullina, “A characterization of subdirectly irreducible acts”, Prikl. Diskr. Mat., 2015, no. 1(27), 5–16

Citation in format AMSBIB

\Bibitem{KozKha15}

\by I.~B.~Kozhukhov, A.~R.~Haliullina

\paper A characterization of subdirectly irreducible acts

\jour Prikl. Diskr. Mat.

\yr 2015

\issue 1(27)

\pages 5--16

\mathnet{http://mi.mathnet.ru/pdm491}

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https://www.mathnet.ru/eng/pdm491

https://www.mathnet.ru/eng/pdm/y2015/i1/p5

This publication is cited in the following 8 articles:

I. B. Kozhukhov, “Kommutativnye polugruppy s ogranichennymi v sovokupnosti poryadkami podpryamo nerazlozhimykh poligonov”, Chebyshevskii sb., 22:1 (2021), 188–199
V. L. Usoltsev, “Podpryamaya nerazlozhimost i atomy reshetok kongruentsii algebr s operatorom i simmetricheskoi osnovnoi operatsiei”, Chebyshevskii sb., 22:2 (2021), 257–270
Usol'tsev V.L., “Subdirectly Irreducible Algebras in One Class of Algebras With One Operator and the Main Near-Unanimity Operation”, Lobachevskii J. Math., 42:1 (2021), 206–216
M. Sedaghatjoo, M. Roueentan, “The structure of subdirectly irreducible and uniform acts over rectangular bands”, Semigr. Forum, 101:1 (2020), 192–201
I. B. Kozhukhov, A. V. Mikhalev, “Acts over semigroups”, J. Math. Sci., 269:3 (2023), 362–401
M. Roueentan, M. Sedaghatjoo, “On uniform acts over semigroups”, Semigr. Forum, 97:2 (2018), 229–243
M. M. Ebrahimi, Kh. Keshvardoost, M. Mahmoudi, “Simple and subdirectly irreducible finitely supported $Cb$ -sets”, Theor. Comput. Sci., 706 (2018), 1–21
G. Moghaddasi, M. Mahmoudi, “Subdirectly irreducible acts over some semigroups”, Bull. Iran Math. Soc., 43:6 (2017), 1913–1924

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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