Let S always denote a semigroup with zero. This paper is devoted to study some of properties zero-divisor graph of S-act. We give several generalizations of the concept of zero-divisor elements in an S-act. Then for each S-act A we associate three undirected (simple) graphs Γ*(A) ⊆ Γ(A) ⊆ Γ*(A). Also we show that if A is an S-act, then
Γ*(A) is a connected graph and diam(Γ*(A)) ≤ 3; and
If Ann(A) is a prime ideal of S, then diam(Γ*(A)) ≤ 2.
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Estaji, A.A., Haghdadi, T. & Estaji, A.A. Zero divisor graphs for S-act. Lobachevskii J Math 36, 1–8 (2015). https://doi.org/10.1134/S1995080215010084
Keywords and phrases
- prime subact
- multiplication S-act
- zero-divisor graph