• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.213-226
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• 2022

Let R be a ring and M an R-module. Then M is said to be regular w-flat provided that the natural homomorphism I ⊗_R M → R ⊗_R M is a w-monomorphism for any regular ideal I. We distinguish regular w-flat modules from regular flat modules and w-flat modules by idealization constructions. Then we give some characterizations of total quotient rings and Prüfer v-multiplication rings (PvMRs for short) utilizing the homological properties of regular w-flat modules.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.67-80
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• 2015

For a pomonoid S, let us denote Pos-S the category of S-posets and S-poset maps. In this paper, we consider the slice category Pos-S/B for an S-poset B, and study some categorical ingredients. We first show that there is no non-trivial injective object in Pos-S/B. Then we investigate injective objects with respect to the class of regular monomorphisms in this category and show that Pos-S/B has enough regular injective objects. We also prove that regular injective objects are retracts of exponentiable objects in this category. One of the main aims of the paper is to draw attention to characterizing injectivity in the category Pos-S/B under a particular case where B has trivial action. Among other things, we also prove that the necessary condition for a map (an object) here to be regular injective is being convex and present an example to show that the converse is not true, in general.