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2013•Journal of Algebra and Its ApplicationsRequires access

ON THE CENTER OF ZERO-DIVISOR AND IDEAL-DIVISOR GRAPHS OF FINITE COMMUTATIVE RINGS

Lane Bloome, Hailee Peck

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Abstract

This paper is concerned with investigating the center and radius of zero-divisor and ideal-divisor graphs of finite commutative rings. In particular, we examine the interplay between the center and cut-sets of zero-divisor graphs. Of interest are conditions that need to be met in order for either of these sets to contain the other. We then explore the radius and central sets of ideal-divisor graphs, particularly the classification of the center via radius results.

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What this paper is about

This paper is concerned with investigating the center and radius of zero-divisor and ideal-divisor graphs of finite commutative rings. In particular, we examine the interplay between the center and cut-sets of zero-divisor graphs. Of interest are conditions that need to be met in order for either of these sets to contain the other. We then explore the radius and central sets of ideal-divisor graphs, particularly the classification of the center via radius results.

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Available abstract

This paper is concerned with investigating the center and radius of zero-divisor and ideal-divisor graphs of finite commutative rings. In particular, we examine the interplay between the center and cut-sets of zero-divisor graphs. Of interest are conditions that need to be met in order for either of these sets to contain the other. We then explore the radius and central sets of ideal-divisor graphs, particularly the classification of the center via radius results.

Key concepts: Zero divisor, Divisor (algebraic geometry), Mathematics, Ideal (ethics), Center (category theory), Zero (linguistics), RADIUS, Combinatorics

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