ZERO-DIVISOR GRAPH OF THE RINGS OF REAL MEASURABLE FUNCTIONS WITH THE MEASURES

Author(s):

H. Hejazipour , A. Naghipour *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

Let M(X,A,μ) be the ring of real-valued measurable functions on a measurable space (X,A) with measure μ. In this paper, we study the zero-divisor graph of M(X,A,μ), denoted by Γ(M(X,A,μ)). We give the relationships among graph properties of Γ(M(X,A,μ)), ring properties of M(X,A,μ) and measure properties of (X,A,μ). Finally, we investigate the continuity properties of Γ(M(X,A,μ)).

Keywords:

Rings of measurable functions , Measure space , zero-divisor graph , Continuous function

Language:
English
Published:
Journal of Algebraic Systems, Volume:9 Issue: 2, Winter-Spring 2022
Pages:
175 to 192
https://www.magiran.com/p2353785