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CLASSIFYING MONOIDS BY QUASI-ANNIHILATOR (HOMO)FLATNESS OF THEIR RIGHT REES FACTORS
Aminizadeh, Reza,Rasouli, Hamid,Tehranian, Abolfazl Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.3
In this paper, the class of quasi-annihilator (homo)flat acts based on the notion of quasi-annihilator ideal is introduced. This class lies strictly between the classes of weakly (homo)flat and principally weakly (homo)flat acts. Some properties of such kinds of flatness are studied. We present some homological classifications for monoids by means of quasiannihilator (homo)flatness of their right Rees factor acts.
AMALGAMATED DUPLICATION OF SOME SPECIAL RINGS
Tavasoli, Elham,Salimi, Maryam,Tehranian, Abolfazl Korean Mathematical Society 2012 대한수학회보 Vol.49 No.5
Let R be a commutative Noetherian ring and let I be an ideal of R. In this paper we study the amalgamated duplication ring $R{\bowtie}I$ which is introduced by D'Anna and Fontana. It is shown that if R is generically Cohen-Macaulay (resp. generically Gorenstein) and I is generically maximal Cohen-Macaulay (resp. generically canonical module), then $R{\bowtie}I$ is generically Cohen-Macaulay (resp. generically Gorenstein). We also de ned generically quasi-Gorenstein ring and we investigate when $R{\bowtie}I$ is generically quasi-Gorenstein. In addition, it is shown that $R{\bowtie}I$ is approximately Cohen-Macaulay if and only if R is approximately Cohen-Macaulay, provided some special conditions. Finally it is shown that if R is approximately Gorenstein, then $R{\bowtie}I$ is approximately Gorenstein.
AMALGAMATED DUPLICATION OF SOME SPECIAL RINGS
Elham Tavasoli,Maryam Salimi,Abolfazl Tehranian 대한수학회 2012 대한수학회보 Vol.49 No.5
Let R be a commutative Noetherian ring and let I be an ideal of R. In this paper we study the amalgamated duplication ring $R{\bowtie}I$ which is introduced by D'Anna and Fontana. It is shown that if R is generically Cohen-Macaulay (resp. generically Gorenstein) and I is generically maximal Cohen-Macaulay (resp. generically canonical module), then $R{\bowtie}I$ is generically Cohen-Macaulay (resp. generically Gorenstein). We also de ned generically quasi-Gorenstein ring and we investigate when $R{\bowtie}I$ is generically quasi-Gorenstein. In addition, it is shown that $R{\bowtie}I$ is approximately Cohen-Macaulay if and only if R is approximately Cohen-Macaulay, provided some special conditions. Finally it is shown that if R is approximately Gorenstein, then $R{\bowtie}I$ is approximately Gorenstein.
Characterization of suzuki group by nse and order of group
Ali Iranmanesh,Hosein Parvizi Mosaed,Abolfazl Tehranian 대한수학회 2016 대한수학회보 Vol.53 No.3
Let $G$ be a finite group and $\nse(G)$ be the set of numbers of elements of $G$ of the same order. In this paper, we prove that the simple group $Sz(2^{2m+1})$, where $2^{2m+1}-1$ is a prime number, is uniquely determined by $\nse(Sz(2^{2m+1}))$ and $|Sz(2^{2m+1})|$.
CHARACTERIZATION OF SUZUKI GROUP BY NSE AND ORDER OF GROUP
Iranmanesh, Ali,Mosaed, Hosein Parvizi,Tehranian, Abolfazl Korean Mathematical Society 2016 대한수학회보 Vol.53 No.3
Let G be a finite group and nse(G) be the set of numbers of elements of G of the same order. In this paper, we prove that the simple group $Sz(2^{2m+1})$, where $2^{2m+1}-1$ is a prime number, is uniquely determined by $nse(Sz(2^{2m+1}))$ and ${\mid}Sz(2^{2m+1}){\mid}$.
Semi-symmetric cubic graph of order $12p^3$
Pooriya Majd Amoli,Mohammad Reza Darafsheh,Abolfazl Tehranian 대한수학회 2022 대한수학회보 Vol.59 No.1
A simple graph is called semi-symmetric if it is regular and edge transitive but not vertex transitive. In this paper we prove that there is no connected cubic semi-symmetric graph of order $12p^3$ for any prime number $p$.