this paper extends the notion of ditopology to the case where openness and closedness are given in terms of {em a priori} unrelated drading functions. the resulting notion of graded ditopology is considered both in the setting of lattices and in that textures, the relation between the two approaches being discussed in detail. interrelations between graded ditopologies and ditopologies on textur...

This paper extends the notion of ditopology to the case where openness and closedness are given in terms of {em a priori} unrelated Drading functions. The resulting notion of graded ditopology is considered both in the setting of lattices and in that textures, the relation between the two approaches being discussed in detail. Interrelations between graded ditopologies and ditopologies on textur...

Graded ditopological texture spaces have been presented and discussed in categorical aspects by Lawrence M. Brown and Alexander {v S}ostak in cite{BS}. In this paper, the authors generalize the structure of diuniformity in ditopological texture spaces defined in cite{OB} to the graded ditopological texture spaces and investigate graded ditopologies generated by graded diuniformities. The autors...

The author considers equivalence direlations and the corresponding quotients of textures, using the interior relation on the texture as a tool in this investigation. A close relationship with surjective difunctions is shown, and the notions of quotient ditopology and quotient difunction are defined and studied. Finally, the existence of a T0 reflection on the category dfDitop is established.

let $g$ be a group with identity $e$. let $r$ be a $g$-graded commutative ring with a non-zero identity and $m$ be a graded $r$-module. in this article, we introduce the concept of graded almost semiprime submodules. also, we investigate some basic properties of graded almost semiprime and graded weakly semiprime submodules and give some characterizations of them.

let r be a g-graded ring and m be a g-graded r-module. in this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.

‎let $g$ be a group with identity $e.$ let $r$ be a $g$-graded‎ ‎commutative ring and $m$ a graded $r$-module‎. ‎in this paper‎, ‎we‎ ‎introduce several results concerning graded classical prime‎ ‎submodules‎. ‎for example‎, ‎we give a characterization of graded‎ ‎classical prime submodules‎. ‎also‎, ‎the relations between graded‎ ‎classical prime and graded prime submodules of $m$ are studied‎.‎

let  be a graded ring and  be a graded -module. we define a topology on graded prime spectrum  of the graded -module  which is analogous to that for , and investigate several properties of the topology.

Let $G$ be a monoid with identity $e$. In this paper, first we introduce the notions of $G$-graded hyperrings, graded hyperideals and graded hyperfields in the sense of Krasner hyperring $R$. Also, we define the notion of a greded $R$-hypermodules and some examples are presented. Then we investigate graded maximal, graded prime and graded primary hyperideals of a graded hyperring $R$. Finally, ...