Let R be a commutative ring with identity and let M unitary R-module. In this paper, we introduce the notion of weakly S-2-absorbing submodule. Suppose that S is multiplicatively closed subset R. A submodule P (P:R M)∩S=∅ said to if there exists an element s ∈ such whenever a,b∈R m∈M 0≠abm∈P, then sab∈(P: M) or sam∈P sbm∈P. We give characterizations, properties examples submodules.

One of the sciences used in digital security systems is cryptography. Cryptography closely related to integer system, especially prime numbers. Prime numbers themselves have been abstracted a lot. form abstraction ideal. Previous studies proven that an Ideal said be ideal on if and only I constructed by element. Other also shown how develops. them research result Dauns, where developed submodul...

Using the notion of fuzzy small submodules of a module, we introduce the concept of fuzzy coessential extension of a fuzzy submodule of a module. We attempt to investigate various properties of fuzzy small submodules of a module. A necessary and sufficient condition for fuzzy small submodules is established. We investigate the nature of fuzzy small submodules of a module under fuzzy direct sum....

In order to obtain more power from photovoltaic (PV) modules under mismatching operating conditions, the submodule-based MPPT technique is an important solution. this technique, since power-voltage (P-V) curve of a submodule cannot be multi-peaked, maximum point (MPP) tracking (MPPT) easily achieved through DC-DC converter connected each submodule. Since P-V in multi-peaked form, can obtained w...