On matrix representations of oversemigroups of semigroups generated by mutually annihilating 2-potent and 2-nilpotent elements
DOI:
https://doi.org/10.17721/1812-5409.2020/3.12Abstract
Among the old results, there are only some results on the representation type of semigroups, namely, for a finite quite simple semigroup (I. S. Ponizovsky) and some semigroups of all transformations of a finite set (I. S. Ponizovsky, C. Ringel); these papers were discussed on finite representation type. If we talk about new results, and even for semigroup classes, then it should be noted works on representations of the semigroups generated by idempotents with partial zero multiplication (V. M. Bondarenko, O. M. Tertychna), semigroups generated by the potential elements (V. M. Bondarenko, O. V. Zubaruk) and representations of direct products of the symmetric second-order semigroup (V. M. Bondarenko, E. M. Kostyshyn). Such semigroups can have both a finite and infinite representation type.
V. M. Bondarenko and Ja. V. Zatsikha described representation types of the third-order semigroups over a field, and indicate the canonical form of the matrix representations for any semigroup of finite representation type. This article is devoted to the study of similar problems for oversemigroups of commutative semigroups.
Key words: field, oversemigroup, defining relations, matrix representations, tame and wild semigroup, semigroup of finite and infinite types, canonical form.
Pages of the article in the issue: 110 - 114
Language of the article: Ukrainian
References
TAMURA, T. (1953). Some remarks on semigroups and all types of semi-groups of order 2, 3. J. Gakugei Tokushima Univ. 3, p. 1–11.
FORSYTHE, G. (1955). SWAC computes 126 distinct semigroups of order 4. Proc. Amer. Math. Soc., 6, p. 443–447.
BONDARENKO, V., ZACIHA, Ja. (2013). Pro vyznachalni spivvidnoshennya dlya minimalnykh system tvirnykh napivhrup tretoho poryadku. Scientific journal of NPU named after M. P. Drahomanov, Series 1, Physics and Mathematics, 14, p. 62–67.
CHOTCHAISTHIT, S. (2014). Simple proofs determining all nonisomorphic semigroups of order 3. Appl. Math. Sci. (Ruse), 8, p. 1261–1269.
BONDARENKO, V., ZACIHA, Ya. (2015). On characteristic properties of semigroups. Algebra Discrete Math., 20, 1, p. 32–39.
BONDARENKO, V., ZACIHA, Ja. (2018). Kanonichni formy matrychnykh zobrazhen napivhrup maloho poryadku. Scientific Bulletin of Uzhhorod University, Series of Mathematics and Informatics, 32, 1, p. 36–49.
DROZD, Yu. (1977). Pro ruchni ta dyki matrychni problemy. Matrix problems – Institute of Math. of AN of Ukrain. SSR, p. 104–114.
BONDARENKO, V., ZUBARUK, O. (2020). Pro matrychni zobrazhennya nadnapivhrup napivhrupy, porodzhenoyi dvoma vzayemno anul’ovnymy idempotentamy. Scientific Bulletin of Uzhhorod University, Series of Mathematics and Informatics, 36, 1. p. 7-15.
KLEINER, M. (1972). O tochnykh predstavleniyakh chastichno uporyadochennykh mnozhestv konechnogo tipa. Zap. Nauch. Semin. LOMI, 28, p. 42–59.
GELFAND, I., PONOMAREV, V. (1968). Nerozkladni zobrazhennya hrupy Lorentsa. Advances in Math. Sciences, 23, 2, p. 3–60.
NAZAROVA, L., ROITER, А., SERGEICHUK, V., BONDARENKO, V. (1972). Primeneniye moduley nad diadoy dlya klassifikatsii konechnykh p-grupp, obladajuschih abelevoj podgruppoj indeksa p, i par vzaimno annulirujuschih operatorov. Zap. nauch. seminarov LOMI., 28, p. 69-92.
BONDARENKO, V. (2003). Linear operators on S-graded vector spaces. Linear algebra Appl., 365, p. 45-90.
RINGEL, C. (1975). The representation type of local algebras. Lecture Notes in Mathematics, 488, p. 282–305.
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