TY - JOUR
T1 - On finite congruence-simple semirings
AU - Monico, Chris
N1 - Funding Information:
The author thanks the anonymous referee for his/her careful reading and valuable input which greatly increased the quality of this work. This research was supported by a fellowship from the Center for Applied Mathematics at the University of Notre Dame, and in part by NSF grant DMS-00-72383.
PY - 2004/1/15
Y1 - 2004/1/15
N2 - In this paper, we describe finite, additively commutative, congruence simple semirings. The main result is that the only such semirings are those of order 2, zero-multiplication rings of prime order, matrix rings over finite fields, ones with trivial addition, and those that are additively idempotent.
AB - In this paper, we describe finite, additively commutative, congruence simple semirings. The main result is that the only such semirings are those of order 2, zero-multiplication rings of prime order, matrix rings over finite fields, ones with trivial addition, and those that are additively idempotent.
KW - Congruence free
KW - Congruence simple
KW - Semirings
UR - http://www.scopus.com/inward/record.url?scp=0347760127&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2003.09.034
DO - 10.1016/j.jalgebra.2003.09.034
M3 - Article
AN - SCOPUS:0347760127
SN - 0021-8693
VL - 271
SP - 846
EP - 854
JO - Journal of Algebra
JF - Journal of Algebra
IS - 2
ER -