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Let R be a commutative ring and Z (R) be its zero-divisors set. The zero-divisor graph of R , denoted by Γ (R) , is an undirected graph with vertex set Z (R) ∗ = Z (R) ∖ { 0 } and two distinct vertices a and b are adjacent if and only if a b = 0. In this paper, for n = p R q S where p and q are primes (p < q) and R and S are positive integers, we calculate the A α spectrum of the graphs Γ (ℤ n). [ABSTRACT FROM AUTHOR]

Our intention in this paper is to prove the following. Let R be a ring with an idempotent element (0; 1 -)e and f be a multiplicative b-generalized derivation on R. Then we show that f is additive by imposing certain conditions on the ring R. [ABSTRACT FROM AUTHOR]

Mesenteric lipomas are very rare intraperitoneal tumors in children. When symptoms like severe abdominal pain, constipation, repe ated vomiting develop, they are brought into medical attention. Despite ambiguous clinical findings, a sonographic suspicion may be further strengthened by CT scan or MRI. However, diagnostic laparotomy with resection of the mass followed by histopathological evaluation may confirm the diagnosis. We report one such rare case of a mesenteric lipoma in an 8 years old girl which may well be among the first 25 cases of mesenteric lipoma in children reported worldwide. [ABSTRACT FROM AUTHOR]