CHARACTERIZATIONS OF GRADED PRÜFER ⋆-MULTIPLICATION DOMAINS

Sahandi, Parviz The Kangwon-Kyungki Mathematical Society 2014 한국수학논문집 Vol.22 No.1

Let $R={\bigoplus}_{\alpha{\in}\Gamma}R_{\alpha}$ be a graded integral domain graded by an arbitrary grading torsionless monoid ${\Gamma}$, and ⋆ be a semistar operation on R. In this paper we define and study the graded integral domain analogue of ⋆-Nagata and Kronecker function rings of R with respect to ⋆. We say that R is a graded Pr$\ddot{u}$fer ⋆-multiplication domain if each nonzero finitely generated homogeneous ideal of R is ⋆$_f$-invertible. Using ⋆-Nagata and Kronecker function rings, we give several different equivalent conditions for R to be a graded Pr$\ddot{u}$fer ⋆-multiplication domain. In particular we give new characterizations for a graded integral domain, to be a $P{\upsilon}MD$.

Simulation of continuous catalytic conversion of glycerol into lactic acid in a microreactor system: A CFD study

Pooya Jalal Sahandi,Mohammad Kazemeini,Samahe Sadjadi 한국공업화학회 2021 Journal of Industrial and Engineering Chemistry Vol.104 No.-

Hand in hand with the flourish of the biodiesel industry, glycerol (GLY) as an inconvenient by-product hasgenerated environmental and sustainability concerns. Devising measures for efficient transformation ofGLY into value-added products is a promising solution. In this contribution, the transformation of GLYto lactic acid (LA) as a valuable chemical was investigated in a continuous process for industrial applications. In this regard, a catalytic method using heterogeneous Cu nanoparticles in NaOH solution was studiedin a microreactor by a CFD simulation. A seven-inlet micromixer comprising an optimized mixing unitwas incorporated for uniform distribution of the species. The effects of various parameters upon the processperformance were considered and the optimum points were determined. Also, the extent of theinfluence of each variable on LA yield was evaluated using sensitivity analysis techniques. While higherLA yield could be obtained at extreme scenarios, optimum values of the Re and temperature for obtainingthe maximum performance under sensible operating conditions were determined to be 0.108 and 510.1 Kwhich led to the optimum yields of 67.8% and 59.5%, respectively. Moreover, the sensitivity analysisrevealed that the molar ratio of OH /GLY and temperature were the most and least significant parameters,respectively.

UPPERS TO ZERO IN POLYNOMIAL RINGS OVER GRADED DOMAINS AND UMt-DOMAINS

Hamdi, Haleh,Sahandi, Parviz Korean Mathematical Society 2018 대한수학회보 Vol.55 No.1

Let $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}\;R_{\alpha}$ be a graded integral domain, H be the set of nonzero homogeneous elements of R, and ${\star}$ be a semistar operation on R. The purpose of this paper is to study the properties of $quasi-Pr{\ddot{u}}fer$ and UMt-domains of graded integral domains. For this reason we study the graded analogue of ${\star}-quasi-Pr{\ddot{u}}fer$ domains called $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. We study several ring-theoretic properties of $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. As an application we give new characterizations of UMt-domains. In particular it is shown that R is a $gr-t-quasi-Pr{\ddot{u}}fer$ domain if and only if R is a UMt-domain if and only if RP is a $quasi-Pr{\ddot{u}}fer$ domain for each homogeneous maximal t-ideal P of R. We also show that R is a UMt-domain if and only if H is a t-splitting set in R[X] if and only if each prime t-ideal Q in R[X] such that $Q{\cap}H ={\emptyset}$ is a maximal t-ideal.

GRADED PRIMITIVE AND INC-EXTENSIONS

Hamdi, Haleh,Sahandi, Parviz Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.2

It is well-known that quasi-$Pr{\ddot{u}}fer$ domains are characterized as those domains D, such that every extension of D inside its quotient field is a primitive extension and that primitive extensions are characterized in terms of INC-extensions. Let $R={\bigoplus}_{{\alpha}{{\in}}{\Gamma}}$ $R_{\alpha}$ be a graded integral domain graded by an arbitrary torsionless grading monoid ${\Gamma}$ and ${\star}$ be a semistar operation on R. The main purpose of this paper is to give new characterizations of gr-${\star}$-quasi-$Pr{\ddot{u}}fer$ domains in terms of graded primitive and INC-extensions. Applications include new characterizations of UMt-domains.

ON ϕ-PSEUDO ALMOST VALUATION RINGS

Esmaeelnezhad, Afsaneh,Sahandi, Parviz Korean Mathematical Society 2015 대한수학회보 Vol.52 No.3

The purpose of this paper is to introduce a new class of rings that is closely related to the classes of pseudo valuation rings (PVRs) and pseudo-almost valuation domains (PAVDs). A commutative ring R is said to be ${\phi}$-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map ${\phi}$ from the total quotient ring T(R) to R localized at Nil(R). A prime ideal P of a ${\phi}$-ring R is said to be a ${\phi}$-pseudo-strongly prime ideal if, whenever $x,y{\in}R_{Nil(R)}$ and $(xy){\phi}(P){\subseteq}{\phi}(P)$, then there exists an integer $m{\geqslant}1$ such that either $x^m{\in}{\phi}(R)$ or $y^m{\phi}(P){\subseteq}{\phi}(P)$. If each prime ideal of R is a ${\phi}$-pseudo strongly prime ideal, then we say that R is a ${\phi}$-pseudo-almost valuation ring (${\phi}$-PAVR). Among the properties of ${\phi}$-PAVRs, we show that a quasilocal ${\phi}$-ring R with regular maximal ideal M is a ${\phi}$-PAVR if and only if V = (M : M) is a ${\phi}$-almost chained ring with maximal ideal $\sqrt{MV}$. We also investigate the overrings of a ${\phi}$-PAVR.

ON φ-PSEUDO ALMOST VALUATION RINGS

Afsaneh Esmaeelnezhad,Parviz Sahandi 대한수학회 2015 대한수학회보 Vol.52 No.3

The purpose of this paper is to introduce a new class of rings that is closely related to the classes of pseudo valuation rings (PVRs) and pseudo-almost valuation domains (PAVDs). A commutative ring R is said to be a φ-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map φ from the total quotient ring T(R) to R localized at Nil(R). A prime ideal P of a φ-ring R is said to be a φ-pseudo-strongly prime ideal if, whenever x, y ∈ RNil(R) and (xy)φ(P) ⊆ φ(P), then there exists an integer m ≥ 1 such that either xm ∈ φ(R) or ymφ(P) ⊆ φ(P). If each prime ideal of R is a φ-pseudo strongly prime ideal, then we say that R is a φ-pseudo-almost valuation ring (φ-PAVR). Among the properties of φ-PAVRs, we show that a quasilocal φ-ring R with regular maximal ideal M is a φ-PAVR if and only if V = (M : M) is a φ-almost chained ring with maximal ideal √MV . We also investigate the overrings of a φ-PAVR.

Graded integral domains in which each nonzero homogeneous ideal is divisorial

장규환,Haleh Hamdi,Parviz Sahandi 대한수학회 2019 대한수학회보 Vol.56 No.4

Let $\Gamma$ be a nonzero commutative cancellative monoid (written additively), $R = \bigoplus_{\alpha\in\Gamma}R_{\alpha}$ be a $\Gamma$-graded integral domain with $R_{\alpha} \neq \{0\}$ for all $\alpha \in \Gamma$, and $S(H) = \{f \in R \,|\, C(f) = R\}$. In this paper, we study homogeneously divisorial domains which are graded integral domains whose nonzero homogeneous ideals are divisorial. Among other things, we show that if $R$ is integrally closed, then $R$ is a homogeneously divisorial domain if and only if $R_{S(H)}$ is an h-local Pr\"ufer domain whose maximal ideals are invertible, if and only if $R$ satisfies the following four conditions: (i) $R$ is a graded-Pr\"{u}fer domain, (ii) every homogeneous maximal ideal of $R$ is invertible, (iii) each nonzero homogeneous prime ideal of $R$ is contained in a unique homogeneous maximal ideal, and (iv) each homogeneous ideal of $R$ has only finitely many minimal prime ideals. We also show that if $R$ is a graded-Noetherian domain, then $R$ is a homogeneously divisorial domain if and only if $R_{S(H)}$ is a divisorial domain of (Krull) dimension one.

Uppers to zero in polynomial rings over graded domains and UM$t$-domains

Haleh Hamdi,Parviz Sahandi 대한수학회 2018 대한수학회보 Vol.55 No.1

Let $R=\bigoplus_{\alpha\in\Gamma}R_{\alpha}$ be a graded integral domain, $H$ be the set of nonzero homogeneous elements of $R$, and $\star$ be a semistar operation on $R$. The purpose of this paper is to study the properties of quasi-Pr\"{u}fer and UM$t$-domains of graded integral domains. For this reason we study the graded analogue of $\star$-quasi-Pr\"{u}fer domains called gr-$\star$-quasi-Pr\"{u}fer domains. We study several ring-theoretic properties of gr-$\star$-quasi-Pr\"{u}fer domains. As an application we give new characterizations of UM$t$-domains. In particular it is shown that $R$ is a gr-$t$-quasi-Pr\"{u}fer domain if and only if $R$ is a UM$t$-domain if and only if $R_P$ is a quasi-Pr\"{u}fer domain for each homogeneous maximal $t$-ideal $P$ of $R$. We also show that $R$ is a UM$t$-domain if and only if $H$ is a $t$-splitting set in $R[X]$ if and only if each prime $t$-ideal $Q$ in $R[X]$ such that $Q\cap H=\emptyset$ is a maximal $t$-ideal.

Interactive illustration of collage for children with folktale e-book

Kang, D.,Tian, F.,Sahandi, R. Ohmsha 2017 Journal of Visualization Vol. No.

AMALGAMATED MODULES ALONG AN IDEAL

El Khalfaoui, Rachida,Mahdou, Najib,Sahandi, Parviz,Shirmohammadi, Nematollah Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.1

Let R and S be two commutative rings, J be an ideal of S and f : R → S be a ring homomorphism. The amalgamation of R and S along J with respect to f, denoted by R ⋈f J, is the special subring of R × S defined by R ⋈f J = {(a, f(a) + j) | a ∈ R, j ∈ J}. In this paper, we study some basic properties of a special kind of R ⋈f J-modules, called the amalgamation of M and N along J with respect to ��, and defined by M ⋈�� JN := {(m, ��(m) + n) | m ∈ M and n ∈ JN}, where �� : M → N is an R-module homomorphism. The new results generalize some known results on the amalgamation of rings and the duplication of a module along an ideal.