| Title:
|
On left $C$-$\scr U$-liberal semigroups (English) |
| Author:
|
He, Yong |
| Author:
|
Shao, Fang |
| Author:
|
Li, Shi-qun |
| Author:
|
Gao, Wei |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
1085-1108 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the equivalence $\tilde{\mathcal Q}^U$ on a semigroup $S$ in terms of a set $U$ of idempotents in $S$ is defined. A semigroup $S$ is called a $\mathcal U$-liberal semigroup with $U$ as the set of projections and denoted by $S(U)$ if every $\tilde{\mathcal Q}^U$-class in it contains an element in $U$. A class of $\mathcal U$-liberal semigroups is characterized and some special cases are considered. (English) |
| Keyword:
|
equivalence $\tilde{\mathcal Q}^U$ |
| Keyword:
|
left $C$-$\mathcal U$-liberal semigroup |
| Keyword:
|
left semi-spined product |
| Keyword:
|
band-formal construction |
| Keyword:
|
left $C$-liberal semigroup |
| MSC:
|
20M10 |
| idZBL:
|
Zbl 1157.20334 |
| idMR:
|
MR2280796 |
| . |
| Date available:
|
2009-09-24T11:41:22Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128132 |
| . |
| Reference:
|
[1] L. Du, Y. He: On the **-Green’s relations of semigroups and $C$-broad semigroups.J. Northwest Univ. (Natural Sci. Edt.) 29 (1999), 9–12. |
| Reference:
|
[2] A. El-Qallali: Structure theory for abundant and related semigroups.PhD. Thesis, , York, 1980. |
| Reference:
|
[3] J. B. Fountain: Rpp monoids with central idempotents.Semigroup Forum 13 (1977), 229–237. 10.1007/BF02194941 |
| Reference:
|
[4] J. B. Fountain: Adequate semigroups.Proc. Edinburgh Math. Soc. 44 (1979), 113–125. Zbl 0414.20048, MR 0549457 |
| Reference:
|
[5] J. B. Fountain: Abundant semigroups.Proc. London Math. Soc. 44 (1982), 103–129. Zbl 0481.20036, MR 0642795 |
| Reference:
|
[6] J. B. Fountain, G. M. S. Gomes, and V. Gould: A Munn type representation for a class of $E$-semiadequate semigroups.J. Algebra 218 (1999), 693–714. MR 1705754, 10.1006/jabr.1999.7871 |
| Reference:
|
[7] G. M. S. Gomes, V. Gould: Fundamental Ehresmann semigroups.Semigroup Forum 63 (2001), 11–33. MR 1830041, 10.1007/s002330010054 |
| Reference:
|
[8] Y. Q. Guo, X. M. Ren, and K. P. Shum: Another structure of left $C$-semigroups.Adv. Math. 24 (1995), 39–43. MR 1334601 |
| Reference:
|
[9] Y. Q. Guo, K. P. Shum, P. Y. Zhu: The structure of left $C$-rpp semigroups.Semigroup Forum 50 (1995), 9–23. MR 1301549, 10.1007/BF02573502 |
| Reference:
|
[10] Y. He: A construction for $\mathcal P$-regular semigroups (announcement).Adv. Math. 29 (2000), 566–568. |
| Reference:
|
[11] Y. He: Partial kernel normal systems in regular semigroups.Semigroup Forum 64 (2002), 325–328. Zbl 1002.20037, MR 1876862, 10.1007/s002330010059 |
| Reference:
|
[12] Y. He: Some studies on regular and generalized regular semigroups.PhD. Thesis, Zhongshan Univ., Guangzhou, 2002. MR 2021655 |
| Reference:
|
[13] Y. He: A construction for $\mathcal P$-regular semigroups.Commun. Algebra 31 (2003), 1–27. MR 1969210, 10.1081/AGB-120016747 |
| Reference:
|
[14] Y. He, Y. Q. Guo, and K. P. Shum: The construction of orthodox supper rpp semigroups.Sci. China 47 (2004), 552–565. MR 2128582, 10.1360/02ys0365 |
| Reference:
|
[15] J. M. Howie: Fundamentals of Semigroup Theory.Oxford University Press Inc., New York, 1995. Zbl 0835.20077, MR 1455373 |
| Reference:
|
[16] M. Kil’p: On monoids over which all strongly flat cyclic right acts are projective.Semigroup Forum 52 (1996), 241–245. Zbl 0844.20051, MR 1371806, 10.1007/BF02574099 |
| Reference:
|
[17] M. V. Lawson: Rees matrix semigroups.Proc. Edinburgh Math. Soc. 33 (1990), 23–37. Zbl 0668.20049, MR 1038762 |
| Reference:
|
[18] M. V. Lawson: Semigroups and ordered categories. I. The reduced case.J. Algebra 141 (1991), 422–462. Zbl 0747.18007, MR 1125706, 10.1016/0021-8693(91)90242-Z |
| Reference:
|
[19] D. B. McAlister: One-to one partial right translations of a right cancellative semigroup.J. Algebra 43 (1976), 231–251. Zbl 0349.20025, MR 0424980, 10.1016/0021-8693(76)90158-7 |
| Reference:
|
[20] M. Petrich: Inverse Semigroups.John Wiley & Sons, New York, 1984. Zbl 0546.20053, MR 0752899 |
| Reference:
|
[21] M. Petrich, N. Reilly: Completely Regular Semigroups.John Wiley & Sons, New York, 1999. MR 1684919 |
| Reference:
|
[22] F. Shao, Y. He: Partial kernel normal systems for eventually regular semigroups.Semigroup Forum 71 (2005), 401–410. Zbl 1098.20046, MR 2204759, 10.1007/s00233-005-0528-7 |
| Reference:
|
[23] X. D. Tang: On a theorem of $C$-wrpp semigroups.Comm. Algebra 25 (1997), 1499–1504. Zbl 0879.20030, MR 1444014, 10.1080/00927879708825931 |
| Reference:
|
[24] M. Yamada: P-systems in regular semigroups.Semigroup Forum 24 (1982), 173–187. Zbl 0479.20030, MR 0650569, 10.1007/BF02572766 |
| Reference:
|
[25] M. Yamada,M. K. Sen: $\mathcal P$-regular semigroups.Semigroup Forum 39 (1989), 157–178. MR 0995827, 10.1007/BF02573295 |
| Reference:
|
[26] M. C. Zhang, Y. He: The structure of $\mathcal P$-regular semigroups.Semigroup Forum 54 (1997), 278–291. MR 1436847, 10.1007/BF02676611 |
| Reference:
|
[27] P. Y. Zhu, Y. Q. Guo, K. P. Shum: Structure and characterizations of left Clifford semigroups.Science in China, Series A 35 (1992), 791–805. MR 1196631 |
| . |
