# Classification of finite congruence-simple semirings with zero

Zumbrägel, J (2008). Classification of finite congruence-simple semirings with zero. Journal of Algebra and its Applications, 7(3):363-377.

## Abstract

Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a dense' subsemiring of the endomorphism semiring of a finite idempotent commutative monoid.
We also investigate those subsemirings further, addressing e.g. the question of isomorphy.

## Abstract

Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a dense' subsemiring of the endomorphism semiring of a finite idempotent commutative monoid.
We also investigate those subsemirings further, addressing e.g. the question of isomorphy.

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