2. Primary ideals in C(X). C(X) denotes the ring of real-valued continuous functions on the topological space X, under ordinary pointwise addition and multiplication. By a primary ideal we mean an ideal which is contained in at most one maximal ideal. An O-ideal is an ideal / such that for each pair/i,/2G/ there exists eEI, depending on/i and f2, such that/<«=/.-, for i = l, 2 [7; 4]. A prime-l...

Linear network coding over finite fields is a wellstudied problem. We consider the more general setting of linear coding for directed acyclic networks with finite commutative ring alphabets. Our results imply that for scalar linear network coding over commutative rings, fields can always be used when the alphabet size is flexible, but other rings may be needed when the alphabet size is fixed. W...

We introduce an iterative method for finding a common element of set of fixed points of nonexpansive mappings, the set of solutions of a finite family of variational inclusion with setvalued maximal monotone mappings and inverse strongly monotone mappings, and the set of solutions of a mixed equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theorems for a...

A graph G(V,E) with vertex set V is said to have a prime labeling if there exist a bijection f : V (G) → {1, 2, . . . , |V |} such that for each edge xy ∈ E(G), f(x) and f(y) are relatively prime. It becomes an interesting problem to investigate the maximum possible edges that can be constructed in a graph with n vertices having prime labeling property. We interpret this problem in number theor...

The main result of this paper states that if R is a right Noetherian right bounded prime ring such that nonzero prime ideals are maximal and such that every proper homomorphic image of R is a principal right ideal ring then R is right hereditary. In [10, Theorem 8] it is proved that if R is a right bounded prime ring of finite right Goldie dimension such that every proper homomorphic image is a...

We provide an upper bound of the dimension of the maximal projective submodule of the Lie module of the symmetric group of n letters in prime characteristic p, where n = pk with p k.

Perfusion techniques and equipment in pediatric open heart surgery have continued to focus on decreasing prime volumes and lowering surface areas of the cardiopulmonary bypass circuit. While this has improved drastically over the last 20 years, greater demand is being placed on the perfusionist to reduce the deleterious effects of bypass without compromising safety or efficiency. Specifically, ...

Abstract Let G be a finite group and assume that of automorphisms A acts on , such the orders are relatively prime. We prove fact imposing certain conditions set maximal -invariant subgroups relating to nilpotency, p -nilpotency, normality or having p’ -order, determines properties structure as solubility, -solubility -nilpotency.

We classify partitions which are of maximal p-weight for all odd primes p. As a consequence, we show that any non-linear irreducible character of the symmetric and alternating groups vanishes on some element of prime order.