No abstract

No abstract

No abstract

Let M be a lattice module over a C-lattice L. A proper element P of M is said to be classical prime if for a, b ∈ L and X ∈ M, abX ≤ P implies that aX ≤ P or bX ≤ P. The set of all classical prime elements of M , Spec cp (M) is called as classical prime spectrum. In this article, we introduce and study a topology on Spec cp (M), called as Zariski-like topology of M. We investigate this topological space from the point of view of spectral spaces. We show that if M has ascending chain condition on classical prime radical elements, then Spec cp (M) with the Zariski-like topology is a spectral space.

<abstract><p>Let $ G_1 \square G_2 $ be the Cartesian product of simple, connected and finite graphs $ G_1 $ and $ G_2 $. We give necessary and sufficient conditions for the Cartesian product of graphs to be very strongly perfect. Further, we introduce and characterize the co-strongly perfect graph. The very strongly perfect graph is implemented in the real-time application of a wireless sensor network to optimize the set of master nodes to communicate and control nodes placed in the field.</p></abstract>