Investigates congruences in Γ-semiring, indicating relationships with operator semirings.
The purpose of this paper is to study different types of congruences such as cancellative congruence, left and right regular congruence, maximal congruence and prime congruence on a Γ-semiring.This study is accomplished via the operator semirings of a Γ-semiring by obtaining various lattice isomorphisms (bijection / inclusion preserving bijection) between the lattice of congruences / cancellative congruences / regular congruences (respectively, maximal congruences / prime congruences) on a Γ-semiring and those on the operator semirings.
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Basu et al. (2026) studied this question.
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