On the Left Inversive Semiring Congruences on Additive Regular Semirings

다국어 초록 (Multilingual Abstract)

An additive regular semiring S is left inversive if the set E+(S) of all
additive idempotents is left regular. The set LC(S) of all left inversive semiring
congruences on an additive regular semiring S is a lattice. The relations µ and k
(resp.), induced by tr and ker (resp.), are congruences on LC(S) and each µ-class
½µ (resp. each k-class ½k) is a complete modular sublattice with ½min and ½max
(resp. with ½min and ½max), as the least and greatest elements. ½min, ½max, ½min and
½max, in particular ²max, the maximum additive idempotent separating congruence
has been characterized explicitly. A semiring is quasi-inversive if and only if it is a subdirect product of a left inversive and a right inversive semiring.

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