TY - JOUR
T1 - Topological Rings and Modules Via Operations
TT -
JF - IJMSI
JO - IJMSI
VL - 16
IS - 2
UR - http://ijmsi.ir/article-1-1208-en.html
Y1 - 2021
SP - 31
EP - 48
KW - Operations
KW - $alpha_{beta}$-Open set
KW - Rins
KW - $alpha_{(beta
KW - beta)}$-Topological rings
KW - $alpha_{(beta
KW - gamma)}$-Topological $R$-modules
N2 - 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.
M3 10.52547/ijmsi.16.2.31
ER -