| Title:
|
One-sided principal ideals in the direct product of two semigroups (English) |
| Author:
|
Fabrici, Imrich |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
118 |
| Issue:
|
4 |
| Year:
|
1993 |
| Pages:
|
337-342 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A necessary and sufficient condition is given for a) a principal left ideal $L(s,t)$ in $S\times T$ to be equal to the direct product of the corresponding principal left ideals $L(s)\times L(t)$, b) an $\Cal L$-class $L_{(s,t)}$ to be equal to the direct product of the corresponding $\Cal L$-classes $L_s\times L_t$. (English) |
| Keyword:
|
principal left ideal |
| Keyword:
|
direct product |
| Keyword:
|
direct product of two semigroups |
| MSC:
|
20M10 |
| MSC:
|
20M12 |
| MSC:
|
20M15 |
| idZBL:
|
Zbl 0810.20043 |
| idMR:
|
MR1251880 |
| DOI:
|
10.21136/MB.1993.126156 |
| . |
| Date available:
|
2009-09-24T21:01:02Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126156 |
| . |
| Reference:
|
[1] Abrhám I.: On (H, T)-ideals in the direct product of semigroups.Mat. časopis 21 (1971), 199-211. |
| Reference:
|
[2] Clifford A.H., Preston G.B.: The algebraic theory of semigroups.American Math. Soc., Providence, R.I., 1961. Zbl 0111.03403, MR 0132791 |
| Reference:
|
[3] Fabrici I.: On semiprime ideals in the direct product of semigroups.Mat. časopis 18 (1968), 201-203. MR 0237674 |
| Reference:
|
[4] Ivan J.: On the direct product of semigroups.Mat.-fyz. časopis (1953), 57-66. MR 0062733 |
| Reference:
|
[5] Petrich M.: Prime ideals in the cartesian product of two semigroups.Czechoslov. Math. J. 12 (1962), 150-152. MR 0140597 |
| Reference:
|
[6] Petrich M.: Introduction to semigroups.Charles E. Merrill Publishing CO. A Bell and Howell Company, Ohio. Zbl 0321.20037, MR 0393206 |
| Reference:
|
[7] Plemmons R.: Maximal ideals in the direct product of two semigroups.Czechoslov. Math. J. 17 (1967), 257-260. Zbl 0189.02001, MR 0214681 |
| . |
