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On left $C$-$\scr U$-liberal semigroups
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 4, pp. 1085-1108
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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.
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.
Classification : 20M10
Keywords: equivalence $\tilde{\mathcal Q}^U$; left $C$-$\mathcal U$-liberal semigroup; left semi-spined product; band-formal construction; left $C$-liberal semigroup 
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He, Yong; Shao, Fang; Li, Shi-qun; Gao, Wei. On left $C$-$\scr U$-liberal semigroups. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 4, pp. 1085-1108. http://geodesic.mathdoc.fr/item/CMJ_2006_56_4_a1/

[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

[4] J. B.  Fountain: Adequate semigroups. Proc. Edinburgh Math. Soc. 44 (1979), 113–125. | MR | Zbl

[5] J. B.  Fountain: Abundant semigroups. Proc. London Math. Soc. 44 (1982), 103–129. | MR | Zbl

[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 | MR

[7] G. M. S.  Gomes, V.  Gould: Fundamental Ehresmann semigroups. Semigroup Forum 63 (2001), 11–33. | DOI | MR

[8] Y. Q.  Guo, X. M.  Ren, and K. P.  Shum: Another structure of left $C$-semigroups. Adv. Math. 24 (1995), 39–43. | MR

[9] Y. Q.  Guo, K. P.  Shum, P. Y.  Zhu: The structure of left $C$-rpp semigroups. Semigroup Forum 50 (1995), 9–23. | DOI | MR

[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 | MR | Zbl

[12] Y.  He: Some studies on regular and generalized regular semigroups. PhD. Thesis, Zhongshan Univ., Guangzhou, 2002. | MR

[13] Y.  He: A construction for $\mathcal P$-regular semigroups. Commun. Algebra 31 (2003), 1–27. | DOI | MR

[14] Y.  He, Y. Q. Guo, and K. P.  Shum: The construction of orthodox supper rpp semigroups. Sci. China 47 (2004), 552–565. | DOI | MR

[15] J. M.  Howie: Fundamentals of Semigroup Theory. Oxford University Press Inc., New York, 1995. | MR | Zbl

[16] M. Kil’p: On monoids over which all strongly flat cyclic right acts are projective. Semigroup Forum 52 (1996), 241–245. | DOI | MR | Zbl

[17] M. V.  Lawson: Rees matrix semigroups. Proc. Edinburgh Math. Soc. 33 (1990), 23–37. | MR | Zbl

[18] M. V. Lawson: Semigroups and ordered categories. I.  The reduced case. J.  Algebra 141 (1991), 422–462. | DOI | MR | Zbl

[19] D. B. McAlister: One-to one partial right translations of a right cancellative semigroup. J.  Algebra 43 (1976), 231–251. | DOI | MR | Zbl

[20] M.  Petrich: Inverse Semigroups. John Wiley & Sons, New York, 1984. | MR | Zbl

[21] M. Petrich, N.  Reilly: Completely Regular Semigroups. John Wiley & Sons, New York, 1999. | MR

[22] F.  Shao, Y.  He: Partial kernel normal systems for eventually regular semigroups. Semigroup Forum 71 (2005), 401–410. | DOI | MR | Zbl

[23] X. D.  Tang: On a theorem of $C$-wrpp semigroups. Comm. Algebra 25 (1997), 1499–1504. | DOI | MR | Zbl

[24] M.  Yamada: P-systems in regular semigroups. Semigroup Forum 24 (1982), 173–187. | DOI | MR | Zbl

[25] M.  Yamada,M. K.  Sen: $\mathcal P$-regular semigroups. Semigroup Forum 39 (1989), 157–178. | DOI | MR

[26] M. C.  Zhang, Y.  He: The structure of $\mathcal P$-regular semigroups. Semigroup Forum 54 (1997), 278–291. | DOI | MR

[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