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. M. Rahimi (Joint with E. Mehdi-Nezhad) Substructures with an almost division algorithm in Euclidean commutator lattices Palestine J. Math. (Accepted) [abstract]

2.	A. M. Rahimi (Joint with E. Mehdi-Nezhad) On weakly firm commutative rings and their connection to the total and zero-divisor graphs Palestine J. Math. (Accepted) [abstract]

3.	A. rahimi (Joint with E. Mehdi-Nezhad) The smarandache vertices of comaximal graph of a commutative ring Libertas Math. (Accepted) [abstract]

4.	A. Rahimi Hyper dice backgammon of finite size Missouri J. Math. Sci. (Accepted) [abstract]

5.	A. Rahimi An elementary approach to the Diophantine equation axm + byn = zr using center of mass Missouri J. Math. Sci. (Accepted) [abstract]

6.	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]

7.	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]

8.	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]

9.	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]

10.	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]

11.	A. M. Rahimi Smarandache vertices of the graphs associated to the commutative rings Comm. Algebra 41 (2013), 1989-2004  [abstract]

12.	D. A. Mojdeh and A. M. Rahimi Dominating sets of some graphs associated to commutative rings Comm. Algebra 40 (2012), 3389-3396  [abstract]

13.	A. M. Rahimi (Joint with E. Mehdi-Nezhad) Euclidean semimodules Libertas Math. 31 (2011), 23-33  [abstract]

14.	A. M. Rahimi (Joint with E. Mehdi-Nezhad) Semirings with an almost division algorithm Libertas Math. 24 (2009), 129-137  [abstract]

15.	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]

16.	A. M. Rahimi A physical approach to Goldbach's conjecture and Fermat's last theorem Libertas Math. 28 (2008), 149-152   [abstract]

17.	Ch. Eslahchi and A. M. Rahimi Some properties of ordered hypergraphs Mat. Vesnik 59 (2007), 9-13  [abstract]

18.	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]

19.	A. M . Rahimi Some Commutative ring results extended to unitary semimodules over commutative semirings Libertas Math. (Accepted) [abstract]

20.	A. M. Rahimi Some results on n-stable rings Missouri J. Math. Sci. 15 (2003), 129-139  [abstract]

21.	A. M. Rahimi A set theoretic property of maximal sublattices Libertas Math. 23 (2003), 53-56  [abstract]

22.	A. M. Rahimi Relative algebraic structures Missouri J. Math. Sci. 14 (2002), 123-135  [abstract]

23.	A. M. Rahimi An application of SB-rings Missouri J. Math. Sci. 14 (2002), 57-58  [abstract]

24.	A. M. Rahimi Euclidian modules Libertas Math. (Accepted) [abstract]