Haddadi, M., Naser Sheykholislami, S. (2019). (r,t)-injectivity in the category $S$-Act. Categories and General Algebraic Structures with Applications, 11(Special Issue Dedicated to Prof. George A. Grätzer), 169-196.

Mahdieh Haddadi; Seyed Mojtaba Naser Sheykholislami. "(r,t)-injectivity in the category $S$-Act". Categories and General Algebraic Structures with Applications, 11, Special Issue Dedicated to Prof. George A. Grätzer, 2019, 169-196.

Haddadi, M., Naser Sheykholislami, S. (2019). '(r,t)-injectivity in the category $S$-Act', Categories and General Algebraic Structures with Applications, 11(Special Issue Dedicated to Prof. George A. Grätzer), pp. 169-196.

Haddadi, M., Naser Sheykholislami, S. (r,t)-injectivity in the category $S$-Act. Categories and General Algebraic Structures with Applications, 2019; 11(Special Issue Dedicated to Prof. George A. Grätzer): 169-196.

^{1}Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.

^{2}Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.

Abstract

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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