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. The smarandache vertices of comaximal graph of a commutative ringLibertas Math. (Accepted) [abstract]
 2. Hyper dice backgammon of finite sizeMissouri J. Math. Sci. (Accepted) [abstract]
 3. A. Rahimi An elementary approach to the Diophantine equation axm + byn = zr using center of massMissouri J. Math. Sci. (Accepted) [abstract]
 4. The annihilation graphs of commutator posets and lattices with respect to an idealJ. Algebra Appl. (Accepted) [abstract]
 5. The annihilation graphs of commutator posets and lattices with respect to an elementJ. Algebra Appl. (Accepted) [abstract]
 6. On some graphs associated to commutative semiringsResults Math. (2015), DOI: 10.1007/s00025-015-0434-6  [abstract]
 7. Dominating sets of the comaximal and ideal-based zero-divisor graphs of the commutative ringsQuaestiones Math. (Accepted) [abstract]
 8. The annihilating-ideal graph of a commutative ring with respect to an idealComm. Algebra 42 (2014), 2269-2284  [abstract]
 9. Smarandache vertices of the graphs associated to the commutative ringsComm. Algebra 41 (2013), 1989-2004  [abstract]
 10. Dominating sets of some graphs associated to commutative ringsComm. Algebra 40 (2012), 3389-3396  [abstract]
 11. Euclidean semimodulesLibertas Math. 31 (2011), 23-33  [abstract]
 12. Semirings with an almost division algorithmLibertas Math. 24 (2009), 129-137  [abstract]
 13. Ston: A novel method for protein three-dimensional structure comparisonComputers in Biology and Medicine 39 (2009), 166-172  [abstract]
 14. A physical approach to Goldbach's conjecture and Fermat's last theoremLibertas Math. 28 (2008), 149-152   [abstract]
 15. Some properties of ordered hypergraphsMat. Vesnik 59 (2007), 9-13  [abstract]
 16. The k-zero-divisor hypergraph of a commutative ringInt. J. Math. Math. Sci. 2007 (2007), 1-15  [abstract]
 17. Some Commutative ring results extended to unitary semimodules over commutative semiringsLibertas Math. (Accepted) [abstract]
 18. Some results on n-stable ringsMissouri J. Math. Sci. 15 (2003), 129-139  [abstract]
 19. A set theoretic property of maximal sublatticesLibertas Math. 23 (2003), 53-56  [abstract]
 20. Relative algebraic structuresMissouri J. Math. Sci. 14 (2002), 123-135  [abstract]
 21. An application of SB-ringsMissouri J. Math. Sci. 14 (2002), 57-58  [abstract]
 22. Euclidian modulesLibertas Math. (Accepted) [abstract]
 [Back]
scroll left or right