A Characterization of Semirings Which Are Subdirect Products of a Distributive Lattice and a Ring |
| |
| Authors: | S Ghosh |
| |
| Institution: | (1) Department of Mathematics, Southwest Normal University, Chongqing, 400715, P. R. China;(2) Department of Mathematics, Chinese University of Hong Kong, Hong Kong, P. R. China;(3) Department of Pure Mathematics, University of Calcutta, Calcutta, 700019, India |
| |
| Abstract: | E -inversive semiring and a Clifford semiring and show that a semiring S is a subdirect product of a distributive lattice and a ring if and only if S is an E-inversive strong distributive lattice of halfrings. Further a Clifford semiring which is, in fact, an inversive subdirect product of a distributive lattice and a ring, is characterized as a strong distributive lattice of rings. Finally, as a consequence of these results we extend a result of Galbiati and Veronesi 2] in the case of Boolean semirings. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
