| Title:
|
On minimal ideals in semigroups with respect to their subsets. I. (English) |
| Author:
|
Abrhan, Imrich |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| 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 |
| DOI:
|
10.21136/MB.1997.126184 |
| . |
| Date available:
|
2009-09-24T21:22:08Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126184 |
| . |
| 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 |
| . |
