Prime Graphs of Polynomials and Power Series Over Noncommutative Rings

Walaa Obaidallah Alqarafi, Wafaa Mohammed Fakieh and Alaa Abdullah Altassan

International Journal of Mathematics and Mathematical Sciences, 2025, vol. 2025, 1-8

Abstract: The prime graph PGR of a ring R is a graph whose vertex set consists of all elements of R. Two elements x,y∈R are adjacent in the graph if and only if xRy=0 or yRx=0. An element a∈R is called a strong zero divisor in R if ab=0 or ba=0 for some nonzero element b∈R. The set of all strong zero divisors is denoted by SR. In this paper, we study the prime graph of a ring R, considering SR as the set of vertices. In this way, we introduce the modified prime graph PG∗R. We then investigate some combinatorial properties of the prime graphs PGRx and PGRx such as completeness, diameter, and girth, where R is a noncommutative ring.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:5232935

DOI: 10.1155/ijmm/5232935

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