Multiplication-Like ‎Modules‎

Subject Areas : International Journal of Industrial Mathematics

مریم احمدی ¹ (Department of Mathematics, University of Hormozgan, Bandar Abbas, Hormozgan, Iran.)
جواد مقدری ² (Department of Mathematics, University of Hormozgan, Bandar Abbas, Hormozgan, Iran.)

Received: 2019-07-11 Accepted : 2021-08-22 Published : 2021-07-01

Keywords: Free modules, Multiplication-like modules, Multiplication modules, Flat modules, Faithfully flat modules,

Abstract :

In this paper we introduce the concept of multiplication-like modules and we obtain some related results. We show that an R-module M is multiplication-like if and only if for each ideal I of R, I = (IM :R M). We prove that any multiplication-like module is faithful and r-multiplication. So we get that any flat and multiplication-like module is faithfully flat.

References:

[1] F. W. Anderson, K. R. Fuller, Rings and categories of modules,Springer-verlag, New York, Berlin, (1974).
[2] S. Annin, Associated and attached primes over noncommutative ring, Phd. thesis, University of California at Berkeley, (2002).
[3] H. Ansari-Toroghy, F. Farshadifar, The dual notion of multiplication modules, Taiwanese J. Math. 11 (2007) 1189-1201.
[4] H. Ansari-Toroghy, F. Farshadifar, Strong comultiplication modules, CMU. J. Nat. Sci. 8 (2009) 105-113.
[5] A. Barnard, Multiplication modules, Journal of Algebra 71 (1981) 174-178.
[6] Z. A. El-Bast, P. F. Smith, Multiplication modules, Comm. Algebra 16 (1988) 755-779.
[7] H. Fazaeli, F. Rashidi, Primary likesubmodules satisfying the primeful property, Transactions on Algebra and its Applications 1 (2015) 43-54.
[8] M. D. Larsen, P. J. Maccarthy, Mulltiplicative Theory of ideals, volume 43, Academic press, INC. London, (1971).
[9] C. P. Lu, M-radicals of submodules in modules, Mathematica Japonica 34 (1989) 211-219.
[10] C. P. Lu, M-radicals of submodules in modules II, Mathematica Japonica 35 (1990) 991-1001.
[11] R. McCasland, M. Moore, Prime submodules, Comm. Algebra 20 (1992) 1803-1817.
[12] A. Nikseresht, H. Sharif, On comultiplication and r-multiplication modules, Journal of Algebraic Systems 2 (2014) 1-19.
[13] L. H. Rowen, Ring Theory, Volume I, Academic pres, INC. San Diego, (1988).
[14] A. A. Tuganbaev, Distributive and Related topics, Gordon and Breach Science Publisher, amsterdam, (1999).
[15] S. Yassemi, The dual notion of prime modules, Arch. Math (Brno) 37 (2001) 273-278.