On minimal ideals in semigroups with respect to their subsets. I
Mathematica Bohemica, Tome 122 (1997) no. 1, pp. 1-12

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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.
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.
DOI : 10.21136/MB.1997.126184
Classification : 20M10, 20M12
Keywords: minimal left ideals with respect to subsets of semigroups; kernels with respect to subsets of semigroups; partial groups
Abrhan, Imrich. On minimal ideals in semigroups with respect to their subsets. I. Mathematica Bohemica, Tome 122 (1997) no. 1, pp. 1-12. doi: 10.21136/MB.1997.126184
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[1] A. H. Clifford G. B. Preston: The algebraic theory of semigroups I, II. Amer. Math Soc., Providence, 1961, 1967.

[2] E. S. Ljapin: Semigroups. FIZMATGIZ. Moskva, 1960. (In Russian.)

[3] A. H. Clifford: Semigroups containing minimal ideals. Amer. J. Math. 70 (1948) 521-526. | DOI | MR | Zbl

[4] A. H. Clifford: Semigroups without nilpotent ideals. Amer. J. Math. 71 (1949), 834-841 | DOI | MR | Zbl

[5] L. Fuchs: On semigroups admitting relative inverses and having minimal ideals. Pbl Math. Debrecen 1 (1950), 227-231. | MR | Zbl

[6] G. B. Preston: Inverse semigroups with minimal right ideals. J. London Math. Soc. 2. (1954), 404-411. | DOI | MR

[7] D. Rees: Note on semigroups. Proc. Cambridge Philos. Soc. 57 (1941), 334-435. | MR

[8] Š. Schwarz: Theory of semigroups. Sborník prác Prír. fak. Slov. univerzity, IV. Bratislava, 1943. (In Slovak.)

[9] Š. Schwarz: On the structure of simple semigroups without zero. Czechoslovak Math. J. 1 (1951), 41-58. (In Russian.) | MR | Zbl

[10] Š. Schwarz: On semigroups having a kernel. Czechoslovak Math. J. 1 (1951), 259-301. (In Russian.) | MR

[11] A. Suschkiewitsch: Über die endlichen Gгuppen ohne Gesetz der eindeutigen Umkehrbarkeit. Math. Ann. 99 (1928), 30-50. | DOI | MR

[12] O. Steinfeld: Über die Quasiideale von Halbgruppen. Publ. Math. Debrecen 4 (1956), 262-275. | MR | Zbl

[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

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