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.

Let Gamma < PSL_2(C) be discrete, cofinite volume, and noncocompact. We prove that for all K > 1, there is a subgroup H K-quasiconformally conjugate to discrete cocompact of PSL_2(R). Along with previous work Kahn Markovic, this proves every finite covolume Kleinian group has nearly Fuchsian surface subgroup.

We study properties of a C2-cofinite vertex operator algebra V = ⊕ ∞ i=0Vi of CFT type. If it is also rational (i.e. all modules are completely reducible) and V ′ ∼= V , then the rigidity of the tensor category of modules has been proved by Huang [11], where V ′ denotes the restricted dual of V . However, when we treat irrational C2cofinite VOAs, the rigidity is too strong, because it is almost...

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...

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....