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Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded 2-classical prime submodules. Various properties of graded 2-classical prime submodules are considered.

This paper is devoted to showing the upper semicontinuity of global attractors associated with the family of nonlinear viscoelastic equations (Formula presented.) in a three-dimensional space, for f growing up to the critical exponent and dependent on ρ ∈ [0,4), as ρ→0+. This equation models extensional vibrations of thin rods with nonlinear material density ϱ(∂tu) = |∂tu|ρ and presence of memory effects. This type of problems has been extensively studied by several authors; the existence of a global attractor with optimal regularity for each ρ ∈ [0,4) were established only recently. The proof involves the optimal regularity of the attractors combined with Hausdorff's measure. Revisado por pares

An operator T acting on a Banach space X satises the property (aw) if σ(T) \ σW(T) = E0a(T), where σW (T) is the Weyl spectrum of T and E0a(T) is the set of all eigenvalues of T of finite multiplicity that are isolated in the approximate point spectrum of T. In this paper we introduce and study two new spectral properties, namely (Saw) and (Sab), in connection with Weyl-Browder type theorems. Among other results, we prove that T satisfies property (Saw) if and only if T satisfies property (aw) and σSBF-+ (T) = σW (T), where σSBF-+ (T) is the upper semi B-Weyl spectrum of T. Un operador T actuando sobre un espacio de Banach X satisface la propiedad (aw) si σ(T) \ σW(T) = E0a(T), donde σW (T) es el espectro de Weyl de T y E0a(T) es el conjunto de todos los autovalores de T de multiplicidad finita que son aislados en el espectro aproximado puntual de T. En este artículo introducimos y estudiamos dos nuevas propiedades espectrales, llamadas (Saw) y (Sab), en conexión con teoremas tipo Weyl-Browder. Entre otros resultados, mostramos que T satisface la propiedad (Saw) si y sólo si T satisface la propiedad (aw) y σSBF-+ (T) = σW (T), donde σSBF-+ (T) es el espectro superiormente semi B-Weyl de T.