Article in volume
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Title:
On some Morita invariant radicals of semirings
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Discussiones Mathematicae - General Algebra and Applications 43(1) (2023) 85-100
Received: 2021-04-06 , Revised: 2021-08-20 , Accepted: 2021-08-23 , Available online: 2023-01-11 , https://doi.org/10.7151/dmgaa.1408
Abstract:
In this paper we prove that if $R$ and $S$ are Morita equivalent
semirings via Morita context $(R,S,P,Q,\theta,\phi)$, then there exists a
one-to-one inclusion preserving correspondence between the set of all prime
((right) strongly prime, uniformly strongly prime) ideals of $R$ and the set
of all prime (resp. (right) strongly prime, uniformly strongly prime)
subsemimodules of $P$. We also show that prime radicals, (right) strongly prime
radicals, uniformly strongly prime radicals are preserved under Morita
equivalence of semirings.
Keywords:
Morita context, Morita equivalence, semiring, semimodule, radical, prime subsemimodule, strongly prime subsemimodule, uniformly strongly prime, subsemimodule
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