RT - Journal Article
T1 - Topological Rings and Modules Via Operations
JF - IJMSI
YR - 2021
JO - IJMSI
VO - 16
IS - 2
UR - http://ijmsi.ir/article-1-1208-en.html
SP - 31
EP - 48
K1 - Operations
K1 - $alpha_{beta}$-Open set
K1 - Rins
K1 - $alpha_{(beta
K1 - beta)}$-Topological rings
K1 - $alpha_{(beta
K1 - gamma)}$-Topological $R$-modules
AB - The structure of an $alpha_{(beta, beta)}$-topological ring is richer in comparison with the structure of an $alpha_{(beta, beta)}$-topological group. The theory of $alpha_{(beta, beta)}$-topological rings has many common features with the theory of $alpha_{(beta, beta)}$-topological groups. Formally, the theory of $alpha_{(beta, beta)}$-topological abelian groups is included in the theory of $alpha_{(beta, beta)}$-topological rings. The purpose of this paper is to introduce and study the concepts of $alpha_{(beta, beta)}$-topological rings and $alpha_{(beta, gamma)}$-topological $R$-modules. we show how they may be introduced by specifying the neighborhoods of zero, and present some basic constructions. We provide fundamental concepts and basic results on $alpha_{(beta, beta)}$-topological rings and $alpha_{(beta, gamma)}$-topological $R$-modules.
LA eng
UL http://ijmsi.ir/article-1-1208-en.html
M3 10.52547/ijmsi.16.2.31
ER -