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IPM
30
YEARS OLD

“Amir Masoud Rahimi”

Email: 

IPM Positions

Non Resident Researcher (non-resident), School of Mathematics
(2006 - Present )

Past IPM Positions

Associate Researcher (non-resident), School of Mathematics
(2003 - 2006)
Associate Researcher (non-resident), School of Mathematics
(2000 - 2002)


Research Activities

All monoids are commutative monoids with the identity element 0. Some basic algebraic properties of submonoids containing 0 are investigated. It is shown that a monoid A satisfies the ascending chain condition on submonoids if and only if every submonoid of A is finitely generated. The intersection of all maximal submonoids of a monoid A is defined to be the Jacobson radical of A. It is shown that every proper submonoid of a finitely generated monoid A is contained in a maximal submonoid of A. Minimal generating sets, rank and the stable range of monoids are defined. In a monoid A, every element outside the Jacobson radical of A belongs to a minimal generating set of A whenever A satisfies the ascending chain condition on submonoids. It is shown that for any positive integer n and any n-stable monoid A, rank(A) n. A version of Nakayama's lemma for finitely generated monoids is proved. Finally, prime, primary, and the radical of submonoids are defined and some of their properties, by applying the injector submonoids, are investigated.

Present Research Project at IPM

Some Commutative Ring Results Extended to a Class of Commutative Monoids

Related Papers

1. A. rahimi (Joint with E. Mehdi-Nezhad)
The smarandache vertices of comaximal graph of a commutative ring
Libertas Math. (Accepted) [abstract]
2. A. Rahimi
Hyper dice backgammon of finite size
Missouri J. Math. Sci. (Accepted) [abstract]
3. A. Rahimi
An elementary approach to the Diophantine equation axm + byn = zr using center of mass
Missouri J. Math. Sci. (Accepted) [abstract]
4. A. M. Rahimi (Joint with E. Mehdi-Nezhad)
The annihilation graphs of commutator posets and lattices with respect to an ideal
J. Algebra Appl. (Accepted) [abstract]
5. A. M. Rahmi (Joint with E. Mehdi-Nezhad)
The annihilation graphs of commutator posets and lattices with respect to an element
J. Algebra Appl. (Accepted) [abstract]
6. A. M. Rahimi (Joint with E. Mehdi-Nezhad)
On some graphs associated to commutative semirings
Results Math. (2015), DOI: 10.1007/s00025-015-0434-6  [abstract]
7. A. M. Rahimi (Joint with E. Mehdi-Nezhad)
Dominating sets of the comaximal and ideal-based zero-divisor graphs of the commutative rings
Quaestiones Math. (Accepted) [abstract]
8. M. Behboodi and A. M. Rahimi (Joint with F. Aliniaeifard and E. Mehdi-Nezhad)
The annihilating-ideal graph of a commutative ring with respect to an ideal
Comm. Algebra 42 (2014), 2269-2284  [abstract]
9. A. M. Rahimi
Smarandache vertices of the graphs associated to the commutative rings
Comm. Algebra 41 (2013), 1989-2004  [abstract]
10. D. A. Mojdeh and A. M. Rahimi
Dominating sets of some graphs associated to commutative rings
Comm. Algebra 40 (2012), 3389-3396  [abstract]
11. A. M. Rahimi (Joint with E. Mehdi-Nezhad)
Euclidean semimodules
Libertas Math. 31 (2011), 23-33  [abstract]
12. A. M. Rahimi (Joint with E. Mehdi-Nezhad)
Semirings with an almost division algorithm
Libertas Math. 24 (2009), 129-137  [abstract]
13. A. M. Rahimi (Joint with Ch. Eslahchi, H. Pezeshk, M. Sadeghi, H. Maboudi Afkham, and Sh. Arab)
Ston: A novel method for protein three-dimensional structure comparison
Computers in Biology and Medicine 39 (2009), 166-172  [abstract]
14. A. M. Rahimi
A physical approach to Goldbach's conjecture and Fermat's last theorem
Libertas Math. 28 (2008), 149-152   [abstract]
15. Ch. Eslahchi and A. M. Rahimi
Some properties of ordered hypergraphs
Mat. Vesnik 59 (2007), 9-13  [abstract]
16. A. M. Rahimi (Joint with Ch. Eslahchi)
The k-zero-divisor hypergraph of a commutative ring
Int. J. Math. Math. Sci. 2007 (2007), 1-15  [abstract]
17. A. M . Rahimi
Some Commutative ring results extended to unitary semimodules over commutative semirings
Libertas Math. (Accepted) [abstract]
18. A. M. Rahimi
Some results on n-stable rings
Missouri J. Math. Sci. 15 (2003), 129-139  [abstract]
19. A. M. Rahimi
A set theoretic property of maximal sublattices
Libertas Math. 23 (2003), 53-56  [abstract]
20. A. M. Rahimi
Relative algebraic structures
Missouri J. Math. Sci. 14 (2002), 123-135  [abstract]
21. A. M. Rahimi
An application of SB-rings
Missouri J. Math. Sci. 14 (2002), 57-58  [abstract]
22. A. M. Rahimi
Euclidian modules
Libertas Math. (Accepted) [abstract]
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