The goal of this discussion is to study the twigged of pure-small (pr-small) sub- moduleof a module W as recirculation of a small sub-module, and we give some basic idiosyncrasy and instances of this kind of sub-module. Also, we give the acquaint of pure radical of a module W (pr-radical) with peculiarities.
In this paper, we define and study z-small quasi-Dedekind as a generalization of small quasi-Dedekind modules. A submodule of -module is called z-small ( if whenever , then . Also, is called a z-small quasi-Dedekind module if for all implies . We also describe some of their properties and characterizations. Finally, some examples are given.
Let R be a commutative ring with identity, and W be a unital (left) R-module. In this paper we introduce and study the concept of a quasi-small prime modules as generalization of small prime modules.
New types of modules named Fully Small Dual Stable Modules and Principally Small Dual Stable are studied and investigated. Both concepts are generalizations of Fully Dual Stable Modules and Principally Dual Stable Modules respectively. Our new concepts coincide when the module is Small Quasi-Projective, and by considering other kind of conditions. Characterizations and relations of these concepts and the concept of Small Duo Modules are investigated, where every fully small dual stable R-module M is small duo and the same for principally small dual stable.
Let Q be a left Module over a ring with identity ℝ. In this paper, we introduced the concept of T-small Quasi-Dedekind Modules as follows, An R-module Q is T-small quasi-Dedekind Module if,
Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
.
Let be a commutative ring with unity and let be a non-zero unitary module. In
this work we present a -small projective module concept as a generalization of small
projective. Also we generalize some properties of small epimorphism to δ-small
epimorphism. We also introduce the notation of δ-small hereditary modules and δ-small
projective covers.
In this paper, we introduce the concept of e-small M-Projective modules as a generalization of M-Projective modules.
Let be a ring with 1 and D is a left module over . In this paper, we study the relationship between essentially small quasi-Dedekind modules with scalar and multiplication modules. We show that if D is a scalar small quasi-prime -module, thus D is an essentially small quasi-Dedekind -module. We also show that if D is a faithful multiplication -module, then D is an essentially small prime -module iff is an essentially small quasi-Dedekind ring.
Background: Breast cancer is the commonest type of malignancy among women worldwide and in Iraq. Tru-cut needle biopsy technique provides adequate tissue for histopathological diagnosis of suspected breast lumps and assessment of hormonal receptors (estrogen, progesterone and HER2neu) prior to surgical operation.
Objectives: To assess estrogen, progesterone andHER2neu expression using breast cancer tissue specimens obtained by tru-cut biopsy, to correlate the findings with clinicopathological parameters of known prognostic significance in breast cancer patients.
Patients and Methods: This prospective study was held within the Main Referral Center for Early Detection of Breast Tumors/Medical City Teachi
Let M be an R-module, where R be a commutative; ring with identity. In this paper, we defined a new kind of submodules, namely T-small quasi-Dedekind module(T-small Q-D-M) and essential T-small quasi-Dedekind module(ET-small Q-D-M). Let T be a proper submodule of an R-module M, M is called an (T-small Q-D-M) if, for all f ∊ End(M), f ≠ 0, implies