In this work, the notion of principally quasi- injective semimodule is introduced, discussing the conditions needed to get properties and characterizations similar or related to the case in modules.

      Let  be an -semimodule with endomorphism semiring Ș. The semimodule  is called principally quasi-injective, if every  -homomorphism from any cyclic subsemimodule of  to  can be extended to an endomorphism of .

This research is a theoretical study that deals with the presentation of the literature of statistical analysis from the perspective of gender or what is called Engendering Statistics. The researcher relied on a number of UN reports as well as some foreign sources to conduct the current study. Gender statistics are defined as statistics that reflect the differences and inequality of the status of women and men overall domains of life, and their importance stems from the fact that it is an important tool in promoting equality as a necessity for the process of sustainable development and the formulation of national and effective development policies and programs. The empowerment of women and the achievement of equality between men and wome

The concept of fully pseudo stable Banach Algebra-module (Banach A-module) which is the generalization of fully stable Banach A-module has been introduced. In this paper we study some properties of fully stable Banach A-module and another characterization of fully pseudo stable Banach A-module has been given.

Objectives: This study aims to evaluate the association between polymorphisms in the promoter region of the tumor necrosis factor-alpha (TNF-α) gene at locations -308G/A, -857C/T, and -863C/A with the tendency of being non-responder to etanercept.

Patients and methods: Between October 2020 and August 2021, a total of 80 patients (10 males, 70 females; mean age: 50 years; range, 30 to 72 years) with rheumatoid arthritis (RA) receiving etanercept for at least six months were included. The patients were divided into two groups responders and non-responders, based on their response after six months of continuous treatment. Following polymerase chain reac

Throughout this paper, T is a ring with identity and F is a unitary left module over T. This paper study the relation between semihollow-lifting modules and semiprojective covers. proposition 5 shows that If T is semihollow-lifting, then every semilocal T-module has semiprojective cover. Also, give a condition under which a quotient of a semihollow-lifting module having a semiprojective cover. proposition 2 shows that if K is a projective module. K is semihollow-lifting if and only if For every submodule A of K with K/( A) is hollow, then K/( A) has a semiprojective cover.

Throughout this paper we introduce the notion of coextending module as a dual of the class of extending modules. Various properties of this class of modules are given, and some relationships between these modules and other related modules are introduced.

In this paper, we introduce and study a new concept named couniform modules, which is a dual notion of uniform modules, where an R-module M is said to be couniform if every proper submodule N of M is either zero or there exists a proper submodule N1 of N such that is small submodule of Also many relationships are given between this class of modules and other related classes of modules. Finally, we consider the hereditary property between R-module M and R-module R in case M is couniform.