A note on prime graph of a finite ring
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Sathyanaryana et al. (2010) introduced the concept of prime graph of an associative ring R and studied some properties in their paper. We found that a correction to be made in the statement of the rst theorem of their paper. In this paper, we investigate some properties of prime graphs of nite rings and give a corrected version of the said result. We establish a formula for nding the number of edges in the prime graph of the ring of residue classes modulo n by using the gcd-sum function. Further, we discuss some results regarding eigenvalues and energy of prime graphs of nite rings.
Abstract
Sathyanaryana et al. (2010) introduced the concept of prime graph of an associative ring R and studied some properties in their paper. We found that a correction to be made in the statement of the rst theorem of their paper. In this paper, we investigate some properties of prime graphs of nite rings and give a corrected version of the said result. We establish a formula for nding the number of edges in the prime graph of the ring of residue classes modulo n by using the gcd-sum function. Further, we discuss some results regarding eigenvalues and energy of prime graphs of nite rings.
참고문헌 (18)
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