International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 9, Pages 539-545

Subdirect products of semirings

P. Mukhopadhyay

Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Calcutta 700019, India

Received 19 July 1999

Copyright © 2001 P. Mukhopadhyay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Bandelt and Petrich (1982) proved that an inversive semiring S is a subdirect product of a distributive lattice and a ring if and only if S satisfies certain conditions. The aim of this paper is to obtain a generalized version of this result. The main purpose of this paper however, is to investigate, what new necessary and sufficient conditions need we impose on an inversive semiring, so that, in its aforesaid representation as a subdirect product, the “ring” involved can be gradually enriched to a “field.” Finally, we provide a construction of full E-inversive semirings, which are subdirect products of a semilattice and a ring.