The duals of annihilator conditions for modules‎

Document Type : Research Paper

Author

Department of Mathematics Education, Farhangian University, P. O. Box 14665-889, Tehran, Iran.

Abstract

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module‎. ‎The purpose of this paper is to introduce and investigate the submodules of an $R$-module $M$ which satisfy the dual of Property $\mathcal{A}$‎, ‎the dual of strong Property $\mathcal{A}$‎, ‎and the dual of proper strong Property $\mathcal{A}$‎. ‎Moreover‎, ‎a submodule $N$ of $M$ which satisfy Property $\mathcal{S_J(N)}$ and Property $\mathcal{I^M_J(N)}$ will be introduced and investigated‎.

Keywords

References

[1] A. Ait Ouahi, S. Bouchiba and M. El-Arabi, On proper strong Property (A) for rings and modules, J. Algebra Appl., 19 No. 12 (2020) 2050239.
[2] D. D. Anderson and S. Chun, Annihilator conditions on modules over commutative rings, J. Algebra Appl., 16 No. 8 (2017) 1750143.
[3] H. Ansari-Toroghy and F. Farshadifar, The dual notion of multiplication modules, Taiwanese J. Math., 11 No. 4 (2007) 1189-1201.
[4] H. Ansari-Toroghy and F. Farshadifar, Comultiplication modules and related results, Honam Math. J., 30 No. 1 (2008) 91-99.
[5] H. Ansari-Toroghy and F. Farshadifar, On comultiplication modules, Korean Ann. Math., 25 No. 1-2 (2008) 57-66.
[6] H. Ansari-Toroghy and F. Farshadifar, The dual notions of some generalizations of prime submodules, Comm. Algebra, 39 No. 7 (2011) 2396-2416.
[7] H. Ansari-Toroghy and F. Farshadifar, Fully idempotent and coidem-potent modules, Bull. Iranian Math. Soc., 38 No. 4 (2012) 987-1005.
[8] H. Ansari-Toroghy and F. Farshadifar, On the dual notion of prime submodules, Algebra Colloq., 19 Special Issue 1 (2012) 1109-1116.
[9] H. Ansari-Toroghy and F. Farshadifar, On the dual notion of prime submodules (II), Mediterr. J. Math., 9 No. 2 (2012) 327-336.
[10] H. Ansari-Toroghy, F. Farshadifar and S.S. Pourmortazavi, On the P-interiors of submodules of Artinian modules, Hacet. J. Math. Stat., 45 No. 3 (2016) 675-682.
[11] M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, Mass. 1969.
[12] A. Barnard, Multiplication modules, J. Algebra, 71 No. 1 (1981) 174-178.
[13] L. Fuchs, W. Heinzer and B. Olberding, Commutative ideal theory without finiteness conditions: Irreducibility in the quotient filed. Abelian groups, rings, modules, and homological algebra, LNPAM, 249 (2006) 121-145.
[14] I. Kaplansky, Commutative rings, In Conference on Commutative Algebra: Lawrence, Kansas 1972, pp. 153-166, Berlin, Heidelberg, Springer Berlin Heidelberg, 2006.
[15] C. -P. Lu, Saturations of submodules, Comm. Algebra, 31 No. 6 (2003) 2655-2673.
[16] R. L. McCasland and P. F. Smith, Generalised associated primes and radicals of submodules, Int. Electron. J. Algebra, 4 (2008) 159-176.
[17] M. Nagata, Local Rings, Interscience Publishers a division of John Wiley Sons, New York, London, 1962.
[18] A. A. Tuganbaev, Multiplication modules, J. Math. Sci. (N.Y.), 123 No. 2 (2004) 3839-3905.
[19] S. Yassemi, Maximal elements of support and cosupport, http://www.ictp.trieste.it/ ̃puboff.
[20] S. Yassemi, Coassociated primes of modules over a commutative ring, Math. Scand, 80 No. 2 (1997) 175-187.
Algebraic Structures and Their Applications
Volume 11, Issue 1
February 2024
Pages 99-113

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