ON 𝜙-SHARP RINGS

Darani, Ahmad Yousefian,Rahmatinia, Mahdi Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.2

The purpose of this paper is to introduce some new class of rings that are closely related to the classes of sharp domains, pseudo-Dededkind domains, TV domains and finite character domains. A ring R is called a ${\phi}$-sharp ring if whenever for nonnil ideals I, A, B of R with $I{\supseteq}AB$, then I = A'B' for nonnil ideals A', B' of R where $A^{\prime}{\supseteq}A$ and $B^{\prime}{\supseteq}B$. We proof that a ${\phi}$-Dedekind ring is a ${\phi}$-sharp ring and we get some properties that by them a ${\phi}$-sharp ring is a ${\phi}$-Dedekind ring.

On Divisorial Submodules

DARANI, AHMAD YOUSEFIAN,RAHMATINIA, MAHDI Department of Mathematics 2015 Kyungpook mathematical journal Vol.55 No.4

This paper is devoted to study the divisorial submodules. We get some equivalent conditions for a submodule to be a divisorial submodule. Also we get equivalent conditions for $(N{\cap}L)^{-1}$ to be a ring, where N, L are submodules of a module M.

On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative Semirings

Darani, Ahmad Yousefian Department of Mathematics 2012 Kyungpook mathematical journal Vol.52 No.1

Let $R$ be a commutative semiring. We define a proper ideal $I$ of $R$ to be 2-absorbing (resp., weakly 2-absorbing) if $abc{\in}I$ (resp., $0{\neq}abc{\in}I$) implies $ab{\in}I$ or $ac{\in}I$ or $bc{\in}I$. We show that a weakly 2-absorbing ideal $I$ with $I^3{\neq}0$ is 2-absorbing. We give a number of results concerning 2-absorbing and weakly 2-absorbing ideals and examples of weakly 2-absorbing ideals. Finally we de ne the concept of 0 - (1-, 2-, 3-)2-absorbing ideals of $R$ and study the relationship among these classes of ideals of $R$.

GRADED PRIMAL SUBMODULES OF GRADED MODULES

Darani, Ahmad Yousefian Korean Mathematical Society 2011 대한수학회지 Vol.48 No.5

Let G be an abelian monoid with identity e. Let R be a G-graded commutative ring, and M a graded R-module. In this paper we first introduce the concept of graded primal submodules of M an give some basic results concerning this class of submodules. Then we characterize the graded primal ideals of the idealization R(+)M.

ON WEAKLY 2-ABSORBING PRIMARY SUBMODULES OF MODULES OVER COMMUTATIVE RINGS

Darani, Ahmad Yousefian,Soheilnia, Fatemeh,Tekir, Unsal,Ulucak, Gulsen Korean Mathematical Society 2017 대한수학회지 Vol.54 No.5

Assume that M is an R-module where R is a commutative ring. A proper submodule N of M is called a weakly 2-absorbing primary submodule of M if $0{\neq}abm{\in}N$ for any $a,b{\in}R$ and $m{\in}M$, then $ab{\in}(N:M)$ or $am{\in}M-rad(N)$ or $bm{\in}M-rad(N)$. In this paper, we extended the concept of weakly 2-absorbing primary ideals of commutative rings to weakly 2-absorbing primary submodules of modules. Among many results, we show that if N is a weakly 2-absorbing primary submodule of M and it satisfies certain condition $0{\neq}I_1I_2K{\subseteq}N$ for some ideals $I_1$, $I_2$ of R and submodule K of M, then $I_1I_2{\subseteq}(N:M)$ or $I_1K{\subseteq}M-rad(N)$ or $I_2K{\subseteq}M-rad(N)$.

Frequency Response Model of Power System in Presence of Thermal, Wind and Hydroelectric Units

Darani Shirin Hassanzadeh,Rabbanifar Payam,Aliabadi Mahmood Hosseini,Radmanesh Hamid 대한전기학회 2023 Journal of Electrical Engineering & Technology Vol.18 No.4

Loss of large generation units or unforeseen changes in consumption load causes disturbances in power system operation. Operators face serious challenges by increasing the penetration level of renewable energies in unit commitment and inability of these resources in providing inertial frequency response. Therefore, having system frequency response model makes operators to have a better understanding of system function and frequency behavior encounter disturbances and critical situations. This paper, studies the importance and necessity of recognizing the frequency response model and presents an integrated model of system frequency response in the presence of thermal, wind and hydroelectric units. Using the Routh stability criterion method, the proposed fifth-order model converts to a second-order model with an acceptable approximation. Proposed system frequency response in a six-bus power system is investigated and effect of changes in the main components on the frequency behavior of system is checked out. Researchers can linearize the obtained frequency response model using conventional linearization methods and use it as a frequency constraint in optimization and security-constrained unit commitment problems. Besides that, frequency behavior of the power system consisting of thermal units after addition of wind and hydroelectric units is studied. This paper helps researchers to have simplified calculation, beneficial and accurate results, while saving time, money and fossil reserves.

ON 𝜙-SCHREIER RINGS

Darani, Ahmad Yousefian,Rahmatinia, Mahdi Korean Mathematical Society 2016 대한수학회지 Vol.53 No.5

Let R be a ring in which Nil(R) is a divided prime ideal of R. Then, for a suitable property X of integral domains, we can define a ${\phi}$-X-ring if R/Nil(R) is an X-domain. This device was introduced by Badawi [8] to study rings with zero divisors with a homomorphic image a particular type of domain. We use it to introduce and study a number of concepts such as ${\phi}$-Schreier rings, ${\phi}$-quasi-Schreier rings, ${\phi}$-almost-rings, ${\phi}$-almost-quasi-Schreier rings, ${\phi}$-GCD rings, ${\phi}$-generalized GCD rings and ${\phi}$-almost GCD rings as rings R with Nil(R) a divided prime ideal of R such that R/Nil(R) is a Schreier domain, quasi-Schreier domain, almost domain, almost-quasi-Schreier domain, GCD domain, generalized GCD domain and almost GCD domain, respectively. We study some generalizations of these concepts, in light of generalizations of these concepts in the domain case, as well. Here a domain D is pre-Schreier if for all $x,y,z{\in}D{\backslash}0$, x | yz in D implies that x = rs where r | y and s | z. An integrally closed pre-Schreier domain was initially called a Schreier domain by Cohn in [15] where it was shown that a GCD domain is a Schreier domain.

GRADED PRIMAL SUBMODULES OF GRADED MODULES

Ahmad Yousefian Darani 대한수학회 2011 대한수학회지 Vol.48 No.5

Let G be an abelian monoid with identity e. Let R be a G-graded commutative ring, and M a graded R-module. In this paper we first introduce the concept of graded primal submodules of M and give some basic results concerning this class of submodules. Then we characterize the graded primal ideals of the idealization R(+)M.

ON WEAKLY 2-ABSORBING PRIMARY SUBMODULES OF MODULES OVER COMMUTATIVE RINGS

Ahmad Yousefian Darani,Fatemeh Soheilnia,Unsal Tekir,Gulsen Ulucak 대한수학회 2017 대한수학회지 Vol.54 No.5

Assume that $M$ is an $R$-module where $R$ is a commutative ring. A proper submodule $N$ of $M$ is called a weakly $2$-absorbing primary submodule of $M $ if $0\neq abm\in N$ for any $a,b\in R$ and $m\in M$, then $ab\in (N:M)$ or $am\in M\mbox{-rad}(N)$ or $bm\in M\mbox{-rad}(N).$ In this paper, we extended the concept of weakly $2$-absorbing primary ideals of commutative rings to weakly $2$-absorbing primary submodules of modules. Among many results, we show that if $N$ is a weakly $2$-absorbing primary submodule of $ M$ and it satisfies certain condition $0\neq I_{1}I_{2}K\subseteq N$ for some ideals $I_{1},I_{2}$ of $R$ and submodule $K$ of $M$, then $ I_{1}I_{2}\subseteq (N:M)$ or $I_{1}K\subseteq M\mbox{-rad}(N)$ or $ I_{2}K\subseteq M\mbox{-rad}(N)$.

On $\phi$-Schreier rings

Ahmad Yousefian Darani,Mahdi Rahmatinia 대한수학회 2016 대한수학회지 Vol.53 No.5

Let $R$ be a ring in which $Nil(R)$ is a divided prime ideal of $R$. Then, for a suitable property $X$ of integral domains, we can define a $\phi$-$X$-ring if $R/Nil(R)$ is an $X$-domain. This device was introduced by Badawi \cite{Ayman1} to study rings with zero divisors with a homomorphic image a particular type of domain. We use it to introduce and study a number of concepts such as $\phi$-Schreier rings, $\phi$-quasi-Schreier rings, $\phi$-almost-rings, $\phi$-almost-quasi-Schreier rings, $\phi$-$GCD$ rings, $\phi$-generalized $GCD$ rings and $\phi$-almost $GCD$ rings as rings $R$ with $Nil(R)$ a divided prime ideal of $R$ such that $R/Nil(R)$ is a Schreier domain, quasi-Schreier domain, almost domain, almost-quasi-Schreier domain, $GCD$ domain, generalized $GCD$ domain and almost $GCD$ domain, respectively. We study some generalizations of these concepts, in light of generalizations of these concepts in the domain case, as well. Here a domain $D$ is pre-Schreier if for all $x, y, z\in D\backslash 0,$ $x\mid yz$ in $D$ implies that $x=rs$ where $r\mid y$ and $s\mid z$. An integrally closed pre-Schreier domain was initially called a Schreier domain by Cohn in \cite{Cohn} where it was shown that a GCD domain is a Schreier domain.