Rees matrix semigroups. (English) Zbl 0668.20049
In this paper we provide a new, abstract characterization of classical Rees matrix semigroups over monoids with zero. The corresponding abstract class of semigroups is obtained by studying the relationship between arbitrary elements and a class of idempotents, which we call projections.
Reviewer: M.V.Lawson
MSC:
| 20M10 | General structure theory for semigroups |
| 20M20 | Semigroups of transformations, relations, partitions, etc. |
References:
| [1] | Batbedat, Simon Stevin 56 pp 181– (1982) |
| [2] | De Barros, Différentielle Catégoriques 11 pp 23– (1969) |
| [3] | DOI: 10.1007/BF01459084 · JFM 54.0151.04 · doi:10.1007/BF01459084 |
| [4] | Steinfeld, Acta. Sci. Math. (Szeged) 28 pp 135– (1967) |
| [5] | DOI: 10.1017/S0305004100017436 · JFM 66.1207.01 · doi:10.1017/S0305004100017436 |
| [6] | DOI: 10.1112/plms/s3-44.1.103 · Zbl 0481.20036 · doi:10.1112/plms/s3-44.1.103 |
| [7] | Marki, Acta. Sci. Math. (Szeged) 37 pp 95– (1975) |
| [8] | Lawson, J. Austral. Math. Soc. Ser. A 42 pp 132– (1987) |
| [9] | Lallement, Acta. Sci. Math. (Szeged) 30 pp 113– (1969) |
| [10] | Lallement, J. Math. Pures Appl. 45 pp 67– (1966) |
| [11] | Howie, An Introduction to the Theory of Semigroups (1976) · Zbl 0355.20056 |
| [12] | Meakin, Colloq. Math. Soc. János Bolyai 39 pp 115– (1981) |
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