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On Strong Dual Rickart Modules

    Gangyong Lee, S. Tariq Rizvi, and Cosmin S. Roman studied Dual Rickart modules. The main purpose of this paper is to define strong dual Rickart module. Let M and N be R- modules , M is called N- strong dual Rickart module (or relatively sd-Rickart to N)which is  denoted by M it is N-sd- Rickart if for every submodule A of M and every homomorphism fHom (M , N) , f (A) is a direct summand of N. We prove that for an R- module M , if R is M-sd- Rickart , then every cyclic submodule of M is a direct summand . In particular, if M is projective, then M is Z-regular. We give various characterizations and basic properties of this type of modules.

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Publication Date
Tue Sep 01 2020
Journal Name
Al-khwarizmi Engineering Journal
UAV Control Based on Dual LQR and Fuzzy-PID Controller

This paper presents the design of a longitudinal controller for an autonomous unmanned aerial vehicle (UAV). This paper proposed the dual loop (inner-outer loop) control based on the intelligent algorithm. The inner feedback loop controller is a Linear Quadratic Regulator (LQR) to provide robust (adaptive) stability. In contrast, the outer loop controller is based on Fuzzy-PID (Proportional, Integral, and Derivative) algorithm to provide reference signal tracking. The proposed dual controller is to control the position (altitude) and velocity (airspeed) of an aircraft. An adaptive Unscented Kalman Filter (AUKF) is employed to track the reference signal and is decreased the Gaussian noise. The mathematical model of aircraft

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Publication Date
Sun Jun 01 2014
Journal Name
Baghdad Science Journal
On Min - Cs Modules and Some Related Concepts

Our aim in this paper is to study the relationships between min-cs modules and some other known generalizations of cs-modules such as ECS-modules, P-extending modules and n-extending modules. Also we introduce and study the relationships between direct sum of mic-cs modules and mc-injectivity.

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Publication Date
Wed Jun 26 2019
Journal Name
Iraqi Journal Of Science
Essentially Second Modules

In this paper, as generalization of second modules we introduce type of modules namely (essentially second modules). A comprehensive study of this class of modules is given, also many results concerned with this type and other related modules presented.

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Publication Date
Sun May 17 2020
Journal Name
Iraqi Journal Of Science
Dual of Extending Acts

Since 1980s, the study of the extending module in the module theory has been a major area of research interest in the ring theory and it has been studied recently by several authors, among them N.V. Dung, D.V. Huyn, P.F. Smith and R. Wisbauer. Because the act theory signifies a generalization of the module theory, the author studied in 2017 the class of extending acts which are referred to as a generalization of quasi-injective acts. The importance of the extending acts motivated us to study a dual of this concept, named the coextending act. An S-act MS is referred to as coextending act if every coclosed subact of Ms is a retract of MS where a subact AS of MS is said to be coclosed in MS if whenever the Rees factor ⁄ is small in th

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Publication Date
Sun May 14 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Annsemimaximal and Coannsemimaximal Modules

        Some authors studied modules with annihilator of every nonzero submodule is prime, primary or maximal. In this paper, we introduce and study annsemimaximal and coannsemimaximal modules, where an R-module M is called annsemimaximal (resp. coannsemimaximal) if annRN (resp. ) is semimaximal ideal of R for each nonzero submodule N of M.

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Publication Date
Thu May 18 2023
Journal Name
Journal Of Engineering
Effect of Cryogenic Trteatment on the Tensile Properties of Carbon Dual Phase Steel

The aim of this study was to evaluate tensile properties of low and medium carbon ferrite -martensite dual phase steel, and the effect cryogenic treatment at liquid nitrogen temperature (-196 ºC) on its properties. Low carbon steel (C12D) and medium carbon steels (C32D & C42D) were used in this work. For each steel grade, five groups of specimens were prepared according to the type of heat treatment. The first group was normalized, the second group was normalized and subsequently subjected to cryogenic treatment then tempered at (200 ºC) for one hour, the third group was quenched from intercritical annealing temperature of (760 ºC) to obtain dual phase (DP) steel, the fourth and fifth groups were both quenched from (760 ºC), but

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Publication Date
Fri Feb 28 2020
Journal Name
Iraqi Journal Of Science
T-Stable-extending Modules and Strongly T- stable Extending Modules

     In this paper we introduce the notions of t-stable extending and strongly t-stable extending modules. We investigate properties and characterizations of each of these concepts. It is shown that a direct sum of t-stable extending modules is t-stable extending while with certain conditions a direct sum of strongly t-stable extending is strongly t-stable extending. Also, it is proved that under certain condition, a stable submodule of t-stable extending (strongly t-stable extending) inherits the property.

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Publication Date
Wed May 17 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
On Fully Semiprime Submodules and Fully Semiprime Modules

   Let R be a commutative ring with unity and let M be a unitary R-module. In this paper we study fully semiprime submodules and fully semiprime modules, where a proper fully invariant R-submodule W of M is called fully semiprime in M if whenever XXW for all fully invariant R-submodule X of M, implies XW.         M is called fully semiprime if (0) is a fully semiprime submodule of M. We give basic properties of these concepts. Also we study the relationships between fully semiprime submodules (modules) and other related submodules (modules) respectively.

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Publication Date
Thu Apr 28 2022
Journal Name
Iraqi Journal Of Science
Generalized Strong Commutativity Preserving Centralizers of Semiprime Rings

Let R be a semiprime ring with center Z(R) and U be a nonzero ideal of R. An additive mappings are called right centralizer if ( ) ( ) and ( ) ( ) holds for all . In the present paper, we introduce the concepts of generalized strong commutativity centralizers preserving and generalized strong cocommutativity preserving centralizers and we prove that R contains a nonzero central ideal if any one of the following conditions holds: (i) ( ) ( ), (ii) [ ( ) ( )] , (iii) [ ( ) ( )] [ ], (iv) ( ) ( ) , (v) ( ) ( ) , (vi) [ ( ) ( )] , (vii) ( ) ( ) ( ), (viii) ( ) ( ) for all .

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Publication Date
Wed Feb 08 2023
Journal Name
Iraqi Journal Of Science
Strongly Cancellation Modules

Let M be an R-module. We introduce in this paper the concept of strongly cancellation module as a generalization of cancellation modules. We give some characterizations about this concept, and some basic properties. We study the direct sum and the localization of this kind of modules. Also we prove that every module over a PID is strongly module and we prove every locally strong module is strongly module.

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