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Title: On minimal ideals in semigroups with respect to their subsets. I. (English)
Author: Abrhan, Imrich
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 122
Issue: 1
Year: 1997
Pages: 1-12
Summary lang: English
Category: math
Summary: In the paper, the following concept are defined: (i) a minimal left (right, two-sided) ideal with respect to a subset $B$ of a semigroup $S$, (ii) a kernel with respect to a subset $B$ of a semigroup $S$, and their basic properties are investigated. (English)
Keyword: minimal left ideals with respect to subsets of semigroups
Keyword: kernels with respect to subsets of semigroups
Keyword: partial groups
MSC: 20M10
MSC: 20M12
idZBL: Zbl 0892.20038
idMR: MR1446395
Date available: 2009-09-24T21:22:08Z
Last updated: 2015-09-15
Stable URL:
Related article:
Reference: [1] A. H. Clifford G. B. Preston: The algebraic theory of semigroups I, II.Amer. Math Soc., Providence, 1961, 1967.
Reference: [2] E. S. Ljapin: Semigroups. FIZMATGIZ.Moskva, 1960. (In Russian.)
Reference: [3] A. H. Clifford: Semigroups containing minimal ideals.Amer. J. Math. 70 (1948) 521-526. Zbl 0038.01103, MR 0025476, 10.2307/2372195
Reference: [4] A. H. Clifford: Semigroups without nilpotent ideals.Amer. J. Math. 71 (1949), 834-841 Zbl 0045.30101, MR 0032661, 10.2307/2372367
Reference: [5] L. Fuchs: On semigroups admitting relative inverses and having minimal ideals.Pbl Math. Debrecen 1 (1950), 227-231. Zbl 0041.35802, MR 0038948
Reference: [6] G. B. Preston: Inverse semigroups with minimal right ideals.J. London Math. Soc. 2. (1954), 404-411. MR 0064037, 10.1112/jlms/s1-29.4.404
Reference: [7] D. Rees: Note on semigroups.Proc. Cambridge Philos. Soc. 57 (1941), 334-435. MR 0005743
Reference: [8] Š. Schwarz: Theory of semigroups.Sborník prác Prír. fak. Slov. univerzity, IV. Bratislava, 1943. (In Slovak.)
Reference: [9] Š. Schwarz: On the structure of simple semigroups without zero.Czechoslovak Math. J. 1 (1951), 41-58. (In Russian.) Zbl 0045.15608, MR 0048428
Reference: [10] Š. Schwarz: On semigroups having a kernel.Czechoslovak Math. J. 1 (1951), 259-301. (In Russian.) MR 0051221
Reference: [11] A. Suschkiewitsch: Über die endlichen Gгuppen ohne Gesetz der eindeutigen Umkehrbarkeit.Math. Ann. 99 (1928), 30-50. MR 1512437, 10.1007/BF01459084
Reference: [12] O. Steinfeld: Über die Quasiideale von Halbgruppen.Publ. Math. Debrecen 4 (1956), 262-275. Zbl 0070.25301, MR 0083998
Reference: [13] I. Abrhan: On J-subalgebras in unary algebras, on simple ideals and J-ideals in grupoids and semigroups.Math. Slovaca 28 (1978), no. 1, 61-80. (In Russian.) MR 0527775


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