\((*,\sim)\)-good congruences on regular ortho-lc-monoids. (English) Zbl 1301.20056
There are known many generalizations of Green’s relations. A new generalization of them was introduced under the name \((*,\sim)\)-Green’s relations by Y. Q. Guo et al., [Commun. Algebra 39, No. 1, 5-31 (2011; Zbl 1247.20068)]. Using this generalization the notion of an orthogroup in the class of regular semigroups was generalized to the notion of an ortho-lc-monoid in the class of \(r\)-ample semigroups. A congruence on a semigroup is called \((*,\sim)\)-good if it preserves the relations \(\mathcal L^*\) and \(\widetilde{\mathcal R}\).
The aim of the paper is “to characterize the \((*,\sim)\)-good congruences on regular ortho-lc-monoids by making use of the compatible congruence systems on the semi-spined product components of regular ortho-lc-monoids”.
The aim of the paper is “to characterize the \((*,\sim)\)-good congruences on regular ortho-lc-monoids by making use of the compatible congruence systems on the semi-spined product components of regular ortho-lc-monoids”.
Reviewer: G. I. Zhitomirskij (Herzliyya)
MSC:
| 20M10 | General structure theory for semigroups |
| 08A30 | Subalgebras, congruence relations |
| 20M17 | Regular semigroups |
| 20M19 | Orthodox semigroups |
Keywords:
generalizations of Green relations; \((*,\sim)\)-Green relations; regular ortho-lc-monoids; good congruences; semi-spined products; idempotentsCitations:
Zbl 1247.20068References:
| [1] | DOI: 10.1007/BF02194941 · Zbl 0353.20051 · doi:10.1007/BF02194941 |
| [2] | DOI: 10.2307/1969317 · Zbl 0043.25601 · doi:10.2307/1969317 |
| [3] | DOI: 10.1007/s13226-010-0030-0 · Zbl 1221.20042 · doi:10.1007/s13226-010-0030-0 |
| [4] | DOI: 10.1081/AGB-100002400 · Zbl 0989.20048 · doi:10.1081/AGB-100002400 |
| [5] | Guo Y.Q., Chinese Science Bulletin 41 (6) pp 462– (1996) |
| [6] | DOI: 10.1007/BF02882566 · Zbl 0903.20035 · doi:10.1007/BF02882566 |
| [7] | DOI: 10.1080/00927870903428247 · Zbl 1247.20068 · doi:10.1080/00927870903428247 |
| [8] | DOI: 10.1007/BF02573502 · Zbl 0821.20046 · doi:10.1007/BF02573502 |
| [9] | Guo Y.Q., Algebra Colloquium 6 (1) pp 105– (1999) |
| [10] | DOI: 10.1017/S0013091500028856 · Zbl 0668.20049 · doi:10.1017/S0013091500028856 |
| [11] | DOI: 10.1007/BF02194891 · Zbl 0299.20057 · doi:10.1007/BF02194891 |
| [12] | DOI: 10.1090/S0002-9939-1987-0877027-2 · doi:10.1090/S0002-9939-1987-0877027-2 |
| [13] | Shum K.P., NJ pp 303– (2008) |
| [14] | DOI: 10.1111/j.1749-6632.1996.tb55645.x · doi:10.1111/j.1749-6632.1996.tb55645.x |
| [15] | Zhu P.Y., Science in China (Series A) 35 (6) pp 791– (1992) |
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