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Keywords:
equivalence $\tilde{\mathcal Q}^U$; left $C$-$\mathcal U$-liberal semigroup; left semi-spined product; band-formal construction; left $C$-liberal semigroup
equivalence $\tilde{\mathcal Q}^U$; left $C$-$\mathcal U$-liberal semigroup; left semi-spined product; band-formal construction; left $C$-liberal semigroup
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.
References:
[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.
[2] A. El-Qallali: Structure theory for abundant and related semigroups. PhD. Thesis, , York, 1980.
[3] J. B. Fountain: Rpp monoids with central idempotents. Semigroup Forum 13 (1977), 229–237. DOI 10.1007/BF02194941
[4] J. B. Fountain: Adequate semigroups. Proc. Edinburgh Math. Soc. 44 (1979), 113–125. MR 0549457 | Zbl 0414.20048
[5] J. B. Fountain: Abundant semigroups. Proc. London Math. Soc. 44 (1982), 103–129. MR 0642795 | Zbl 0481.20036
[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. DOI 10.1006/jabr.1999.7871 | MR 1705754
[7] G. M. S. Gomes, V. Gould: Fundamental Ehresmann semigroups. Semigroup Forum 63 (2001), 11–33. DOI 10.1007/s002330010054 | MR 1830041
[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
[9] Y. Q. Guo, K. P. Shum, P. Y. Zhu: The structure of left $C$-rpp semigroups. Semigroup Forum 50 (1995), 9–23. DOI 10.1007/BF02573502 | MR 1301549
[10] Y. He: A construction for $\mathcal P$-regular semigroups (announcement). Adv. Math. 29 (2000), 566–568.
[11] Y. He: Partial kernel normal systems in regular semigroups. Semigroup Forum 64 (2002), 325–328. DOI 10.1007/s002330010059 | MR 1876862 | Zbl 1002.20037
[12] Y. He: Some studies on regular and generalized regular semigroups. PhD. Thesis, Zhongshan Univ., Guangzhou, 2002. MR 2021655
[13] Y. He: A construction for $\mathcal P$-regular semigroups. Commun. Algebra 31 (2003), 1–27. DOI 10.1081/AGB-120016747 | MR 1969210
[14] Y. He, Y. Q. Guo, and K. P. Shum: The construction of orthodox supper rpp semigroups. Sci. China 47 (2004), 552–565. DOI 10.1360/02ys0365 | MR 2128582
[15] J. M. Howie: Fundamentals of Semigroup Theory. Oxford University Press Inc., New York, 1995. MR 1455373 | Zbl 0835.20077
[16] M. Kil’p: On monoids over which all strongly flat cyclic right acts are projective. Semigroup Forum 52 (1996), 241–245. DOI 10.1007/BF02574099 | MR 1371806 | Zbl 0844.20051
[17] M. V. Lawson: Rees matrix semigroups. Proc. Edinburgh Math. Soc. 33 (1990), 23–37. MR 1038762 | Zbl 0668.20049
[18] M. V. Lawson: Semigroups and ordered categories. I. The reduced case. J. Algebra 141 (1991), 422–462. DOI 10.1016/0021-8693(91)90242-Z | MR 1125706 | Zbl 0747.18007
[19] D. B. McAlister: One-to one partial right translations of a right cancellative semigroup. J. Algebra 43 (1976), 231–251. DOI 10.1016/0021-8693(76)90158-7 | MR 0424980 | Zbl 0349.20025
[20] M. Petrich: Inverse Semigroups. John Wiley & Sons, New York, 1984. MR 0752899 | Zbl 0546.20053
[21] M. Petrich, N. Reilly: Completely Regular Semigroups. John Wiley & Sons, New York, 1999. MR 1684919
[22] F. Shao, Y. He: Partial kernel normal systems for eventually regular semigroups. Semigroup Forum 71 (2005), 401–410. DOI 10.1007/s00233-005-0528-7 | MR 2204759 | Zbl 1098.20046
[23] X. D. Tang: On a theorem of $C$-wrpp semigroups. Comm. Algebra 25 (1997), 1499–1504. DOI 10.1080/00927879708825931 | MR 1444014 | Zbl 0879.20030
[24] M. Yamada: P-systems in regular semigroups. Semigroup Forum 24 (1982), 173–187. DOI 10.1007/BF02572766 | MR 0650569 | Zbl 0479.20030
[25] M. Yamada,M. K. Sen: $\mathcal P$-regular semigroups. Semigroup Forum 39 (1989), 157–178. DOI 10.1007/BF02573295 | MR 0995827
[26] M. C. Zhang, Y. He: The structure of $\mathcal P$-regular semigroups. Semigroup Forum 54 (1997), 278–291. DOI 10.1007/BF02676611 | MR 1436847
[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
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