Title: | On special Rees matrix semigroups over semigroups (English) |
Author: | Nagy, Attila |
Author: | Tóth, Csaba |
Language: | English |
Journal: | Commentationes Mathematicae Universitatis Carolinae |
ISSN: | 0010-2628 (print) |
ISSN: | 1213-7243 (online) |
Volume: | 64 |
Issue: | 3 |
Year: | 2023 |
Pages: | 279-288 |
Summary lang: | English |
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Category: | math |
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Summary: | We study the right regular representation of special Rees matrix semigroups over semigroups, and discuss their embedding in idempotent-free left simple semigroups. (English) |
Keyword: | semigroup |
Keyword: | Rees matrix semigroup |
Keyword: | representation of semigroups |
MSC: | 20M10 |
MSC: | 20M30 |
idZBL: | Zbl 07830509 |
idMR: | MR4717502 |
DOI: | 10.14712/1213-7243.2023.024 |
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Date available: | 2024-03-18T10:37:01Z |
Last updated: | 2024-08-02 |
Stable URL: | http://hdl.handle.net/10338.dmlcz/152299 |
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Reference: | [1] Ayik H., Ruškuc N.: Generators and relations of Rees matrix semigroups.Proc. Edinburgh Math. Soc. (2) 42 (1999), no. 3, 481–495. MR 1721767 |
Reference: | [2] Chrislock J. L.: Semigroups whose regular representation is a group.Proc. Japan Acad. 40 (1964), no. 10, 799–800. MR 0179275 |
Reference: | [3] Chrislock J. L.: Semigroups whose regular representation is a right group.Amer. Math. Monthly 74 (1967), no. 9, 1097–1100. MR 0227295, 10.2307/2313623 |
Reference: | [4] Clifford A. H., Preston G. B.: The Algebraic Theory of Semigroups. Vol. I.Math. Surveys, 7, American Mathematical Society, Providence, 1961. MR 0132791 |
Reference: | [5] Clifford A. H., Preston G. B.: The Algebraic Theory of Semigroups. Vol. II.Math. Surveys, 7, American Mathematical Society, Providence, 1967. MR 0218472 |
Reference: | [6] Cohn P. M.: Embeddings in semigroups with one-sided division.J. London Math. Soc. 31 (1956), no. 2, 169–181. MR 0079007, 10.1112/jlms/s1-31.2.169 |
Reference: | [7] Croisot R.: Demi-groupes simple inversifs à gauche.C. R. Acad. Sci. Paris 239 (1954), 845–847 (French). MR 0064035 |
Reference: | [8] Descalço L., Ruškuc N.: On automatic Rees matrix semigroups.Comm. Algebra 30 (2002), no. 3, 1207–1226. MR 1892597, 10.1080/00927870209342378 |
Reference: | [9] Howie J. M.: An Introduction to Semigroup Theory.L. M. S. Monographs, 7, Academic Press, London, 1976. Zbl 0355.20056, MR 0466355 |
Reference: | [10] Kambites M.: The loop problem for Rees matrix semigroups.Semigroup Forum 76 (2008), no. 2, 204–216. MR 2377584, 10.1007/s00233-007-9016-6 |
Reference: | [11] Kehayopulu N., Tsingelis M.: Ordered semigroups which are both right commutative and right cancellative.Semigroup Forum 84 (2012), no. 3, 562–568. MR 2917192, 10.1007/s00233-011-9346-2 |
Reference: | [12] Lawson M. V.: Rees matrix semigroups.Proc. Edinburgh Math. Soc. (2) 33 (1990), no. 1, 23–37. MR 1038762 |
Reference: | [13] McAlister D. B.: Rees matrix covers for locally inverse semigroups.Trans. Amer. Math. Soc. 227 (1983), no. 2, 727–738. MR 0694385, 10.1090/S0002-9947-1983-0694385-3 |
Reference: | [14] Nagy A.: Subdirectly irreducible right commutative semigroups.Semigroup Forum 46 (1993), no. 2, 187–198. MR 1200213, 10.1007/BF02573565 |
Reference: | [15] Nagy A.: Right commutative $\Delta$-semigroups.Acta Sci. Math. (Szeged) 66 (2000), no. 1–2, 33–46. MR 1768852 |
Reference: | [16] Nagy A.: Special Classes of Semigroups.Adv. Math. (Dordr.), 1, Kluwer Academic Publishers, Dordrecht, 2001. MR 1777265 |
Reference: | [17] Nagy A.: A supplement to my paper “Right commutative $\Delta$-semigroups".Acta Sci. Math. (Szeged) 71 (2005), no. 1–2, 35–36. MR 2160353 |
Reference: | [18] Nagy A.: Medial permutable semigroups of the first kind.Semigroup Forum 76 (2008), no. 2, 297–308. MR 2377591, 10.1007/s00233-007-9027-3 |
Reference: | [19] Nagy A.: Left reductive congruences on semigroups.Semigroup Forum 87 (2013), no. 1, 129–148. MR 3079776, 10.1007/s00233-012-9428-9 |
Reference: | [20] Nagy A.: Remarks on the paper “M. Kolibiar, On a construction of semigroups".Period. Math. Hungar. 71 (2015), no. 2, 261–264. MR 3421700, 10.1007/s10998-015-0094-z |
Reference: | [21] Nagy A.: Left equalizer simple semigroups.Acta Math. Hungar. 148 (2016), no. 2, 300–311. MR 3498533, 10.1007/s10474-015-0578-6 |
Reference: | [22] Nagy A.: A construction of left equalizer simple medial semigroups.Period. Math. Hungar. 86 (2023), no. 1, 37–42. MR 4554111, 10.1007/s10998-022-00454-w |
Reference: | [23] Nagy A., Nagy O.: A construction of semigroups whose elements are middle units.International Journal of Algebra 14 (2020), no. 3, 163–169. 10.12988/ija.2020.91248 |
Reference: | [24] Nagy A., Tóth C.: On the probability that two elements of a finite semigroup have the same right matrix.Comment. Math. Univ. Carolin. 63 (2022), no. 1, 21–31. MR 4445735 |
Reference: | [25] Petrich M.: Lectures in Semigroups.Math. Lehrbücher Monogr. I. Abt. Math. Lehrbücher, 29, Academie-Verlag, Berlin, 1977. MR 0447437 |
Reference: | [26] Petrich M.: Embedding semigroups into idempotent generated ones.Monatsh. Math. 141 (2004), no. 4, 315–322. MR 2053656, 10.1007/s00605-003-0040-7 |
Reference: | [27] Rees D.: On semi-groups.Proc. Cambridge Philos. Soc. 36 (1940), no. 4, 387–400. MR 0002893 |
Reference: | [28] Teissier M.: Sur les demi-groupes ne contenant pas d'élément idempotent.C. R. Acad. Sci. Paris 237 (1953), 1375–1377 (French). MR 0059902 |
Reference: | [29] Tóth C.: Right regular triples of semigroups.available at arXiv:2211.06600v1 [math.GR] (2022), 13 pages. MR 4666108 |
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