Primitive $\pi$-regular semigroups
Miroslav Ćirić, Stojan Bogdanović · Proceedings of the Japan Academy Series A Mathematical Sciences · 1992
In this note we investigate the structure of zr-regular semigroups, the nonzero idempotents of which are primitive.Various characterizations for primitive regular semigroups have been obtained by T. E. Hall [4], G. Lallement and M. Petrich [6], G. B. Preston [7], O. Steinfeld [8] and P. S. Venkatesan [9], [10](this appeared also in the book of A. H. Clifford and G. B. Preston [3]).J. Fountain[ 5] considered primitive abundant semigroups.In this paper we consider primitive r-regular semi- groups and in this way we generalize the previous results for primitive regu- lar semigroups.Throughout this paper, Z '+ will denote the set of all positive integers.If