(r,t)-injectivity in the category $S$-Act | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 11، دوره 11، Special Issue Dedicated to Prof. George A. Grätzer، مهر 2019، صفحه 169-196 اصل مقاله (783.85 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.29252/cgasa.11.1.169 | ||
| نویسندگان | ||
| Mahdieh Haddadi* 1؛ Seyed Mojtaba Naser Sheykholislami2 | ||
| 1Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran. | ||
| 2Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Injectivity؛ $S$-act؛ Hoehnke radical | ||
| مراجع | ||
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