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Welcome to Dr. Mahmood Behboodi

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Office : Postal Code 84156-8311, Room 12 , Department of Mathematical of Scinces Email : mbehbood@cc.iut.ac.ir Phone : (+98)-311-3913612 Fax : (+98)-311-3913602 Web Site : Mahmood Behboodi

Professor

Research Fields : Ring theory (both commutative and non-commutative):

Generalizations of the Wedderburn-Artin theorem and related topics

Virtually uniserial modules and rings related topics

Direct sum decompositions of modules and related topics

Finite representation type of algebras

Prime and classical prime submodules

Classical primary decomposition of rings and modules

Structure and representation of finite rings

Spectral spaces and classical Zariski topology of rings and modules

Teaching

Recent Publications

67. M. Behboodi (Joint wuth E. Bigdeli) Commutative rings whose proper ideals are P-virtually semisimple Bull. Iranian Math. Soc. 48 (2022), 1-12

68. M. Behboodi and A. Moradzadeh-Dehkordi (Joint with M. Qourchi Nejadi) Direct sum decompositions of projective and injective modules into virtually uniserial modules Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116 (2022), 1-11

[16]. Solving an Open Problem of K¨othe on Rings,53nd Annual Iranian Mathematics Conference,Behshahr, Iran.

66. M. Behboodi and A. Moradzadeh-Dehkordi (Joint with M. Qourchi Nejadi) Virtually homo-uniserial modules and rings Comm. Algebra 49 (2021), 3837-3849

64- M. Behboodi and A. Moradzadeh-Dehkordi (Joint with M. Qourchi Nejadi) Virtually uniserial modules and rings J. Algebra 549 (2020), 365-385

65- M. Behboodi (Joint with A. Daneshvar and M. R. Vedadi) Structure of virtually semisimple modules over commutative rings Comm. Algebra (2020), DOI: 10.1080/00927872.2020.1723611

61- M. Behboodi (Joint with S. Roointan-Isfahani) Local rings whose modules are almost serial J. Pure Appl. Algebra (2019), 223, 369-379

62- M. Behboodi (Joint with Z. Fazelpour) Prime uniserial modules and rings J. Algebra Appl. (2019), 18 (2), 1950035

63- M. Behboodi (Joint with E. Bigdeli) Prime virtually semisimple modules and rings Comm. Algebra (2019), 47(10), DOI: 10.1080/00927872.2019.1576184

58- M. Behboodi (Joint with A. Daneshvar and M. R. Vedadi) Virtually semisimple modules and a generalization of the Wedderburn-Artin Theorem Comm. Algebra (2018), 46 (6), 2384-2395

59- M. Behboodi (Joint with A. Daneshvar and M. R. Vedadi) Several generalizations of the Wedderburn-Artin theorem with applications Algebr. Represent Theor. (2018), 21 (6), 1333-1342

60- M. Behboodi (Joint with Sh. Asgari) Commutative rings whose proper ideals are direct sums of uniform modules Comm. Algebra 46 (2018), 1277-1286

55- M. Behboodi (Joint with Z. Fazelpour, and M. R. Vedadi) Rings all of whose prime serial modules are serial J. Algebra Appl. 16 (2017), 1-20

56- M. Behboodi (Joint with S. Heidari) Commutative rings whose proper ideals are serial Algebr. Represent Theor. 20 (2017), 1531-1544

57- M. Behboodi (Joint with Z. Fazelpour), Noetherian rings whose modules are prime serial,Algebr. Represent Theor. 20 (2017), 245-255

51. M. Behboodi (Joint with G. Behboodi Eskandari) On rings over which every finitely generated module is a direct sum of cyclic modules Hacettepe J. Math. Statis. 45 (2016), 1335-1342

54- M. Behboodi (Joint with S. Heidari) Commutative rings whose maximal ideals are direct sums of completely cyclic modules Mathematical Reports 18 (2016), 609-617

52. M. Behboodi (Joint with S. Roointan-Isfahani) Almost uniserial rings and modules J. Algebra 446 (2016), 176-187

53. M. Behboodi (Joint with S. Heidari and S. Roointan-Isfahani) Commutative rings whose proper ideals are direct sum of completely cyclic modules J. Algebra Appl. 15 (2016), # 12 Pages

[15]. Virtualy semisimple modules and two generalizations of Wedderburn-Artin and Krull-Schmidt Theorems with applications,47 Annual Iranian Mathematics Conference,Karaj, Iran

50. M. Behboodi (Joint with F. Aliniaeifard) The annihilating-ideal graph of a ring J. Korean Math. Soc. 52 (2015), 1323-1336

44 - M. Behboodi (Joint with M. Aghasi and M. Zabzevari) A Structure Sheaf on the Spectrum of Prime Radical Modules,

48. M. Behboodi (Joint with G. Behboodi Eskandari) Local duo rings whose finitely generated modules are direct sums of cyclics Indian J. Pure Appl. Math. 46 (2015), 59-72

49. M. Behboodi (Joint with R. Taheri and A. Tehranian) The spectrum subgraph of the annihilating-ideal graph of a commutative ring J. Algebra Appl. 14 (2015), # 19 pages

45 - M. Behboodi (Joint with F. Couchot and S. H. Shojaee), Sigma-Semi-Compact Rings and Modules, J. Algebra Appl. (Accepted) (ISI)

36 - M. Behboodi (Joint with F. Aliniaeifard, E. Mehdi-Nezhad and A. M. Rahimi), The annihilating-ideal graph of a commutative ring with respect to an ideal, Comm. Algebra 42 (2014), 2269-2284.(ISI)

37 - M. Behboodi (with Gh. Aalipour, S. Akbari, R. Nikandish, M.J. Nikmehr, F. Shaveisi), The classification of the annihilating- ideal graph of a commutative ring. Algebra Colloquium 21(2) (2014), 249-256. (ISI)

35 - M. Behboodi (Joint with Z. Nazemian and A. Ghorbani), Uniserial dimension of modules, Journal of Algebra 399 (2014) 894–903 (ISI)

46- M. Behboodi (Joint with S.H. Shojaee) Commutative local rings whose ideals are direct sum of cyclic modules Algebr. Represent Theor. 17 (2014), 971-982

47. M. Behboodi (Joint with M. Arabi-Kakavand) Modules whose classical prime submodules are intersections of maximal submodules Bull. Korean Math. Soc. 51 (2014), 253-266

43 - M. Behboodi (Joint with G. Behboodi Eskandari) Local duo-rings whose finitely generated modules are direct sums of cyclics, Indian J. Pure and Appl. Math. (Accepted) (ISI)

40 - M. Behboodi (Joint with S. H. Shojaee), Commutative local rings whose ideals are direct sum of cyclic modules, Algebr. Represent Theor. (2013), DOI: 10.1007/s10468-013-9427-x

42- M. Behboodi (Joint with G. Behboodi Eskandari) On rings over which every finitely generated module is a direct sum of cyclic modules, Hacettepe J. Mathematics and Statistics (Accepted) (ISI)

39 - M. Behboodi (Joint with M. Arabi-Kakavand), Modules whose classical prime submodules are intersections of maximal submodules,Bull. Korean Math. Soc. 51 (1) (2014) , 253-266. (ISI)

38 - M. Behboodi (Joint with A. Ghorbani, A. Moradzadeh-Dehkordi, and S.H. Shojaee)و On FC-purity and I-purity of modules and Kothe rings, Comm. Algebra 42 (2014), 2061-2081.(ISI)

33 - M. Behboodi (Joint with R. Beyranvand, A. Hashemi, and H. Khabazian), Classification of finite rings: Theory and algorithm, Czechoslovak Math. J. (Accepted)

32 - M. Behboodi (Joint with A. Ghorbani and S.H. Shojaee), (m,n)-algebraically compactness for modules and (m,n)-pure injectivity, Bull. Iranian Math. Soc. (Accepted)

41. M. Behboodi (Joint with R. Jahani-Nezhad, M. H. Naderi), Quasi-Primary Decomposition in Modules Over Proufer Domains, J. Algebraic Systems, 1 (2) (2013), 149-160 .

31 - M. Behboodi (with A. Ghorbani, A. Moradzadeh-Dehkordi, and S. H. Shojaee) C-pure projective modules, Comm. Algebra 41 (2013), 4559-4575. (ISI)

34 - M. Behboodi (Joint with J. A. Beachy and F. Yazdi), Prime M-Ideals, M-Prime submodules, M-Prime radical and M-Baer's lower nilradical of modules, J. Korean Math. Soc. 50 (2013), 1271-1290

M. Behboodi, Rings for which certain modules are direct sums of Cyclics, 23 th Iranian Algebra Seminar, Khansar, 21-22 November 2013, Page 55.

26 - M. Behboodi, On prime modules and dense submodules, J. Commut. Algebra 4 (2012), 479-488 (ISI)

25 - M. Behboodi (with A. Moadzadeh-Dehkordi), On commutative rings whose prime ideals are direct sum of cyclics, Arch. Math. 48 (2012), 291–299.

24 - M. Behboodi (with A.Ghorbani, A.Moradzadeh-Dehkordi, S.H.Shojaee), On left Kothe rings and a generalization of the Kothe-Cohen-Kaplansky theorem, Proc. Amer. Math. Soc. (Accepted). (ISI)

23 - M. Behboodi, Zero divisor graphs of modules over a commutative rings, Journal of Commutative Algebra, 4 (2) (2012), 175-197. (ISI)

30 - M. Behboodi (with M. Baziar, H. Sharif ), Uniformly classical primary submodules, Comm. Algebra 40 (2012) 3192–3201. (ISI)

29 -M. Behboodi (with F. Ali-Niaeifard), Commutative rings whose zero-divisor graphs have positive genus, Comm. Algebra 41 (2012), 3629-3634. (ISI)

28 - M. Behboodi (with F. Ali-Niaeifard), Rings whose annihilating-ideal graphs have positive genus, J. Algebra Appl. 11 (2012), #P13 . (ISI)

27 - M. Behboodi (with M. Mollakarimi), Multiplication modules with Krull dimension, Turk. J. Math., 36, (2012), 550-559. (ISI)

21 - M. Behboodi (with A.Ghorbani, A.Moradzadeh-Dehkordi), Commutative Noetherian local rings whose ideals are direct sums of cyclic modules, J. Algebra, 345 (2011) 257–265. (ISI)

[2]. M. Behboodi, (with A Ghorbani, A. Moradzadeh-Dehkordi and S.H Shojaee) FC-Pure Injectivity and FC-Pure Flatness, 42th Annual Iranian Mathematics Conference Rafsanjan (2011), 53-56. September, 2011

20 - M. Behboodi (with Z. Rakee), The annhilating-ideal graph of commutative rings I. J. Algebra Appl. 10 (4) (2011), 727-739. (ISI)

[1]. Commutative rings whose ideals are direct sums of principal ideals, 42th Annual Iranian Mathematics Conference Rafsanjan (2011), 49-52. September, 2011

19 - M. Behboodi (with Z. Rakee), The annhilating-ideal graph of commutative rings II. J. Algebra Appl. 10 (4) (2011), 740-753. (ISI)

22 - M. Behboodi (with R. Jahani-Nezhad, M. H. Naderi), Classical quasi-primary submodules, Bull. Iranian Math. Soc. 37 (2011), 45-65 . (ISI)

[3]. M. Behboodi, (with M. Arabi-Kakavand) A Generalizations of Hilbert rings to modules, 21th Seminal on Algebra, Tabriz, 2010, pp. 58-61. September, 2010

[4]. M. Behboodi, Some graphs associated to certain algebraic structures, The Second Conference on Algebraic Combinatorics, May 12.13, (2010) Mashhad, Iran, Page 13

[5]. M. Behboodi (with F. Yazdi), Classical prime M-ideals and classical M-prime submodules, 21th Seminal on Algebra, Tabriz, 2010, pp. 250-252. September, 2010

12 - M. Behboodi (with S. H. Shojaee), A generalization of the Zariski topology of arbitrary rings for modules, East-West J. Math. 11(2), (2009), 165-183

[6]. M. Behboodi, Relationship between prime modules and p-modules, 39th Annual Iranian Mathematics Conference Kerman (2008). September, 2008

[7]. M. Behboodi, Classical prime radical of modules and a generalization of Bear's lower radical for modules, 38th Annual Iranian Mathematics Conferences, 3-6 September 2007, pp. 13-15. September, 2007

[10]. M. Behboodi, Classical Zariski topology for modules, 18th Seminar on Algebra. Damghan University of Basic Sciences, 4-5 April, 2006.

[8]. M. Behboodi, Generalizations of the zero divisor graphs of commutative rings to modules, 37-th Anuall Iranian Mathematics Conference, 2-5 September 2006, pp. 634-637. September, 2006

[9]. M. Behboodi, Classical prime modules over commutative rings, 2th Seminar on Commutative Algebra, 2006, IPM, Tehran, Iran. September, 2006

[9]. M. Behboodi, Classical prime modules over commutative rings, 2th Seminar on Commutative Algebra, 2006, IPM, Tehran, Iran. September, 2006

[11]. M. Behboodi, On primeless modules and rings whose nonzero modules have prime submodules, 36th Anuall Iranian Mathematics Conference, 10-13 September 2005 pp. 44.

[12]. M. Behboodi (with Baziar), Weakly primary submodules, 35th Annual Iranian Mathematics Conference January 26-29, 2005 Ahvaz, Iran. August, 2005

[13]. M. Behboodi, The Zariski topology on the weakly prime spectrum of a module, 35th Annual Iranian Mathematics Conference January 26-29, 2005 Ahvaz, Iran. August, 2005

[14]. M. Behboodi, Fully prime modules, 12th Seminar on Algebra. Alzahra University, Tehran, Iran, 4-5, September, 2002