The categories of lattice-valued maps, equalities, free objects, and $\mathcal C$-reticulation

نویسندگان
Karimi Feizabadi, Abolghasem ID 1

1 Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran.

doi
10.29252/cgasa.11.1.93
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