n-copure submodules of modules
n-copure submodules of modules
Let $R$ be a commutative ring, $M$ an $R$-module, and n>=1 an integer. In this paper, we will introduce the concept of n-copure submodules of $M$ as a generalization of copure submodules and obtain some related results.
___
- [1] M.M. Ali and D.J. Smith, Pure submodules of multiplication modules, Beiträge Algebra Geom. 45 (1) (2004)61–74.
- [2] Y. Al-Shaniafi and P. F. Smith, Comultiplication modules over commutative rings, J. Commut. Algebra, 3 (1)(2011), 1-29.
- [3] W. Anderson and K.R. Fuller, Rings and Categories of Modules, Springer-Verlag, New York-Heidelberg-Berlin,1974.
- [4] H. Ansari-Toroghy and F. Farshadifar, The dual notion of multiplication modules, Taiwanese J. Math. 11 (4) (2007)1189–1201.
- [5] H. Ansari-Toroghy and F. Farshadifar, Product and dual product of submodules, Far East J. Math. Sci., 25 (3)(2007), 447–455.
- [6] H. Ansari-Toroghy and F. Farshadifar, Strong comultiplication modules, CMU. J. Nat. Sci. 8 (1) (2009), 105–113.
- [7] H. Ansari-Toroghy and F. Farshadifar, Fully idempotent and coidempotent modules, Bull. Iranian Math. Soc. 38(4) (2012), 987-1005.
- [8] A. Barnard, Multiplication modules, J. Algebra, 71 (1981), 174–178.
- [9] P. M. Cohn, On the free product of associative rings, Math. Z. 71 (1959) 380–398.
- [10] F. Farshadifar, n-pure submodules, submitted.
- [11] F. Farshadifar, Copure and 2-absorbing copure submodules, submitted.
- [12] L. Fuchs, W. Heinzer, and B. Olberding, Commutative ideal theory without finiteness conditions: Irreducibility inthe quotient filed, in : Abelian Groups, Rings, Modules, and Homological Algebra, Lect. Notes Pure Appl. Math.249 (2006), 121–145.
- [13] T. Y. Lam, Lectures on Modules and Rings. Springer 1999.
- [14] P. Ribenboim, Algebraic Numbers. Wiley 1972.
- [15] R. Y. Sharp, Step in commutative algebra, Cambridge University Press, 1990.
- [16] R. Wisbauer, Foundations of Modules and Rings Theory, Gordon and Breach, Philadelphia, PA, 1991.