Spined products of some semigroups
Miroslav Ćirić, Stojan Bogdanović · Proceedings of the Japan Academy Series A Mathematical Sciences · 1993
Spined products of semigroups were first defined and studied by N. Kimura, 1958, [7].After that, spined products have been considered many a time, predominantly those of a band and a semilattice of semigroups with re- spect to their common semilattice homomorphic image.Spined and subdirect products of a band and a semilattice of groups are studied by M. Yamada [13], [14], J. M. Howie and G. Lallement [6] and by M. Petrich [10]; spined products of a band and some types of semilattices of monoids are studied by F. Pastijn [8], A. E1-Qallali [3], [4], and by R. J. Warne [12].For other consid- erations of these products, we refer to [4], [5], [7], [9], [15].In the quoted pap- ers, spined products are considered in connection with some types of bands of semigroups.In this paper, we give a general composition for bands of semigroups that are (punched) spined products of a band and a semilattice of semigroups.This composition, in some sense, is a generalization of a well-known semilattice composition (see Theorem III 7.2.[9]).Let B be a band.By -- ji j, and by _< we denote the natural order on