(r,t)-injectivity in the category $S$-Act

Document Type : Research Paper


Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.



In this paper, we show that injectivity with respect to the class $\mathcal{D}$  of dense monomorphisms of an idempotent and weakly hereditary closure operator of an arbitrary category  well-behaves. Indeed, if $\mathcal{M}$ is a subclass of monomorphisms, $\mathcal{M}\cap \mathcal{D}$-injectivity  well-behaves. We also introduce the notion of $(r,t)$-injectivity in the category {\bf S-Act}, where $r$ and $t$ are Hoehnke radicals, and discuss whether this kind of injectivity well-behaves.


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