TY - JOUR ID - 76601 TI - (r,t)-injectivity in the category $S$-Act JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Haddadi, Mahdieh AU - Naser Sheykholislami, Seyed Mojtaba AD - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran. AD - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran. Y1 - 2019 PY - 2019 VL - 11 IS - Special Issue Dedicated to Prof. George A. Grätzer SP - 169 EP - 196 KW - Injectivity KW - $S$-act KW - Hoehnke radical DO - 10.29252/cgasa.11.1.169 N2 - 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. UR - https://cgasa.sbu.ac.ir/article_76601.html L1 - https://cgasa.sbu.ac.ir/article_76601_35b108e0967457882abe5232f68aa727.pdf ER -