In this paper, we introduce and investigate the notion of projection invariant semisimple modules. Some structural properties aforementioned class modules are studied. We obtain indecomposable decompositions former under some module theoretical conditions. Moreover, explore when finite exchange property implies full for Finally, that endomorphism ring a is ?- Baer ring.

in this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. in fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. some examples are provided to verify the effectiveness and applicability of our results.

The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity co...

In this paper, the definition of meet-continuity on $L$-directedcomplete posets (for short, $L$-dcpos) is introduced. As ageneralization of meet-continuity on crisp dcpos, meet-continuity on$L$-dcpos, based on the generalized Scott topology, ischaracterized. In particular, it is shown that every continuous$L$-dcpo is meet-continuous and $L$-continuous retracts ofmeet-continuous $L$-dcpos are al...

In this paper, the two parameter ADK entropy, as a generalized of Re'nyi entropy, is considered and some properties of it, are investigated. We will see that the ADK entropy for continuous random variables is invariant under a location and is not invariant under a scale transformation of the random variable. Furthermore, the joint ADK entropy, conditional ADK entropy, and chain rule of this ent...