let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

In this paper we investigate non-central elements of the Iwahori-Hecke algebra of the symmetric group whose squares are central. In particular, we describe a commutative subalgebra generated by certain non-central square roots of central elements, and the generic existence of a rank-three submodule of the Hecke algebra contained in the square root of the centre, but not in the centre. The gener...

This article introduces the concept of S-2-absorbing primary submodule as a generalization 2-absorbing submodule. Let S be multiplicatively closed subset ring R and M an R-module. A proper N is said to if (N :R M) ? = there exists fixed element s such that whenever abm for some a,b m M, then either sam or sbm sab ?(N M). We give several examples, properties characterizations related concept. Mo...

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...

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...

In this article, we formalize some basic facts of Z-module. In the first section, we discuss the rank of submodule of Z-module and its properties. Especially, we formally prove that the rank of any Z-module is equal to or more than that of its submodules, and vice versa, there exists a submodule with any given rank that satisfies the above condition. In the next section, we mention basic facts ...