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Fuzzy projective modules and tensor products in fuzzy module categories | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 8، دوره 11، شماره 2، تیر 2014، صفحه 89-101 اصل مقاله (428.04 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2014.1504 | ||
| نویسنده | ||
| Hongxing Liu* | ||
| School of Mathematical Sciences, Shandong Normal University, 250014, Jinan, P. R. China | ||
| چکیده | ||
| Let $R$ be a commutative ring. We write $\mbox{Hom}(\mu_A, \nu_B)$ for the set of all fuzzy $R$-morphisms from $\mu_A$ to $\nu_B$, where $\mu_A$ and $\nu_B$ are two fuzzy $R$-modules. We make $\mbox{Hom}(\mu_A, \nu_B)$ into fuzzy $R$-module by redefining a function $\alpha:\mbox{Hom}(\mu_A, \nu_B)\longrightarrow [0,1]$. We study the properties of the functor $\mbox{Hom}(\mu_A,-):FR\mbox{-Mod}\rightarrow FR\mbox{-Mod}$ and get some unexpected results. In addition, we prove that $\mbox{Hom}(\xi_p,-)$ is exact if and only if $\xi_P$ is a fuzzy projective $R$-module, when $R$ is a commutative semiperfect ring. Finally, we investigate tensor product of two fuzzy $R$-modules and get some related properties. Also, we study the relationships between Hom functor and tensor functor. | ||
| کلیدواژهها | ||
| Fuzzy set؛ Hom functor؛ Fuzzy projective $R$-module؛ Fuzzy $R$-module؛ Tensor product؛ functor | ||
| مراجع | ||
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