The categories of lattice-valued maps, equalities, free objects, and $\mathcal C$-reticulation | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 7، دوره 11، Special Issue Dedicated to Prof. George A. Grätzer، مهر 2019، صفحه 93-112 اصل مقاله (670.29 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.29252/cgasa.11.1.93 | ||
| نویسنده | ||
| Abolghasem Karimi Feizabadi | ||
| Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran. | ||
| چکیده | ||
| In this paper, we study the concept of $\mathcal C$-reticulation for the category $\mathcal C$ whose objects are lattice-valued maps. The relation between the free objects in $\mathcal C$ and the $\mathcal C$-reticulation of rings and modules is discussed. Also, a method to construct $\mathcal C$-reticulation is presented, in the case where $\mathcal C$ is equational. Some relations between the concepts reticulation and satisfying equalities and inequalities are studied. | ||
| کلیدواژهها | ||
| Free object؛ $ell$-ring؛ $ell$-module؛ frame؛ cozero map؛ semi-cozero map؛ the $F$-Zariski topology؛ $mathcal C$-reticulation؛ lattice-valued map | ||
| مراجع | ||
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