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Izvestiya: Mathematics, 2020, Volume 84, Issue 2, Pages 291–323
DOI: https://doi.org/10.1070/IM8869 (Mi im8869) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Conditions of modularity of the congruence lattice of an act over a rectangular band

I. B. Kozhukhovab, A. M. Pryanichnikovac, A. R. Simakovad

a National Research University of Electronic Technology
b Lomonosov Moscow State University
c "Kaskad"
d Innovation Group "I-Teco"
English version PDF (737 kB) Citations (3)
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DOI: https://doi.org/10.1070/IM8869
Abstract: We describe polygons over rectangular bands that have modular, distributive or linearly ordered congruence lattice. It turns out that such polygons have at most 11 elements, and their congruence lattice has at most 300 elements. Furthermore, certain facts are established about the structure of polygons with modular congruence lattice over an arbitrary semigroup and about the structure of the congruence lattice of a polygon over a rectangular band. The work is based on the description of polygons over a completely (0-)simple semigroup obtained by Avdeev and Kozhukhov in 2000 and on the characterization of disconnected polygons with modular or distributive congruence lattice by Ptakhov and Stepanova in 2013.
Keywords: polygon over a semigroup, rectangular band, congruence lattice, modular lattice.
Received: 26.09.2018
Revised: 27.02.2019
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2020, Volume 84, Issue 2, Pages 90–125
DOI: https://doi.org/10.4213/im8869
Bibliographic databases:
Document Type: Article
UDC: 512.579 + 512.567.5
MSC: 06B10, 08B10
Language: English
Original paper language: Russian
Citation: I. B. Kozhukhov, A. M. Pryanichnikov, A. R. Simakova, “Conditions of modularity of the congruence lattice of an act over a rectangular band”, Izv. RAN. Ser. Mat., 84:2 (2020), 90–125; Izv. Math., 84:2 (2020), 291–323
Citation in format AMSBIB
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\paper Conditions of~modularity of~the congruence~lattice of~an~act over a~rectangular band
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:327
    Russian version PDF:63
    English version PDF:31
    References:24
    First page:16
     
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