×
Abrhan, Imrich

On minimal ideals in semigroups with respect to their subsets. II. (English) Zbl 0820.20076

Math. Slovaca 44, No. 4, 463-478 (1994).
The concepts of partial left groups and completely simple semigroups with respect to a subset of a semigroup are introduced. The structures of a) minimal left ideals with respect to a set, b) partial left groups, c) completely simple semigroups with respect to their subsets, are investigated.
Reviewer: V.Fleischer (Tartu)

Cited in 1 Review

MSC:

20M99 Semigroups
20M10 General structure theory for semigroups
20M12 Ideal theory for semigroups

Keywords:

partial left groups; completely simple semigroups; minimal left ideals
PDF BibTeX XML Cite
\textit{I. Abrhan}, Math. Slovaca 44, No. 4, 463--478 (1994; Zbl 0820.20076)
Full Text: EuDML
  • logo of hbz
  • logo of WorldCat

References:

[1] CLIFFORD A. H., PRESTON G. B.: The Algebraic Theory of Semigroups. Vol. I; Vol. II, Amer. Math. Soc., Providence, R.I., 1961; 1967. · Zbl 0111.03403
[2] CLIFFORD A. H.: Semigroups admitting relative inverses. Ann. of Math. 42 (1941). 1037-1049. · Zbl 0063.00920
[3] CLIFFORD A. H.: Semigroups containing minimal ideals. Amer. J. Math. 70 (1948). 521-526. · Zbl 0038.01103
[4] CLIFFORD A. H.: Semigroups without nilpotent ideals. Amer. J. Math.71 (1949). 834-844. · Zbl 0045.30101
[5] IVAN J.: On a decomposition of simple semigroups to direct product. (Slovak). Mat. Čas. 4 (1954), 181-201.
[6] LYAPIN E. S.: Semigroups. (Russian), Nauka, Moskva, 1960. · Zbl 0128.02703
[7] REES D.: Note on semigroups. Math. Proc. Cambridge Philos. Soc. 37 (1941). 334- 435. · Zbl 0063.06456
[8] SCHWARZ S.: Theory of semigroups. (Slovak), Sborník Prírodov. Fak. Slov. Univ. no. 6 (1943), 1-64.
[9] SCHWARZ S.: A structure of simple semigroups without zero. (Russian). Czechoslovak Math. J. 1(76) (1951), 51-65.
[10] SCHWARZ S.: On semigroups having a kernel. (Russian), Czechoslovak Math. J. 1(76) (1951), 259-301.
[11] SUSCHEWITSCH A.: Über die endlichen Gruppen ohne Gesetz der eindestigen Umkehrbarkeit. Math. Ann. 99 (1982), 30-50.
[12] ABRHAN I.: On J-subalgebras in unary algebras on simple ideals and J-ideals in groupoids and semigroups. (Russian), Math. Slovaca 28 (1978), 61-80. · Zbl 0384.08004
[13] ABRHAN I.: On minimal ideals of semigroups with respect to their subsets. I. Math. Bohemica · Zbl 0892.20038
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.