Petrich, Mario Regular semigroups which are subdirect products of a band and a semilattice of groups. (English) Zbl 0257.20055 Glasg. Math. J. 14, 27-49 (1973). Summary: The paper contains various results on the semigroups defined in the title. These semigroups are precisely orthodox bands of groups. A regular semigroup is a subdirect product of a band (= an idempotent semigroup) and a group if and only if it is a band of groups and its subset of idempotents is unitary. Regular semigroups which are subdirect products of a rectangular band and a semilattice of groups are characterized. Each of these and other classes of regular semigroups are presented as certain standard subdirect products (usually spined products) of bands and semilattices of groups, the theorems of equivalence for such presentations are established. Reviewer: Boris M. Schein Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 13 Documents MSC: 20M17 Regular semigroups 20M19 Orthodox semigroups 06A12 Semilattices Keywords:orthodox bands of groups PDFBibTeX XMLCite \textit{M. Petrich}, Glasg. Math. J. 14, 27--49 (1973; Zbl 0257.20055) Full Text: DOI References: [1] DOI: 10.1112/plms/s3-10.1.409 · Zbl 0228.20035 · doi:10.1112/plms/s3-10.1.409 [2] Clifford, The algebraic theory of semigroups I (1961) [3] DOI: 10.2307/2031968 · Zbl 0055.25001 · doi:10.2307/2031968 [4] DOI: 10.2307/2035688 · Zbl 0205.01903 · doi:10.2307/2035688 [5] DOI: 10.3792/pja/1195524790 · Zbl 0081.25501 · doi:10.3792/pja/1195524790 [6] Yamada, Pacific J. Math. 21 pp 371– (1967) · Zbl 0154.01603 · doi:10.2140/pjm.1967.21.371 [7] Howie, Proc. Glasgow Math. Assoc. 7 pp 145– (1966) [8] DOI: 10.2307/1996308 · Zbl 0257.20056 · doi:10.2307/1996308 [9] Petrich, Notices Amer. Math. Soc. 12 pp 619– (1965) [10] Petrich, Portugal. Math. 25 pp 15– (1966) [11] DOI: 10.1007/BF01114879 · Zbl 0124.25801 · doi:10.1007/BF01114879 [12] Petrich, Acad. Roy. Belg. Bull. Cl. Sci. 49 pp 785– (1963) [13] Kimura, Pacific J. Math. 8 pp 257– (1958) · Zbl 0084.02702 · doi:10.2140/pjm.1958.8.257 [14] Yamada, Bull. Shimane Univ. 13 pp 128– (1964) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.