Title & Authors

Abstract
Let G be an abelian monoid with identity e. Let R be a G-graded commutative ring, and M a graded R-module. In this paper we first introduce the concept of graded primal submodules of M an give some basic results concerning this class of submodules. Then we characterize the graded primal ideals of the idealization R(+)M.
Keywords
Language
English
Cited by
References
1.
D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra 1 (2009), no. 1, 3-56.

2.
J. Dauns, Primal modules, Comm. Algebra, 25 (1997), no. 8, 2409-2435.

3.
S. Ebrahimi Atani, On graded weakly prime ideals, Turkish J. Math. 30 (2006), no. 4, 351-358.

4.
S. Ebrahimi Atani, On graded prime submodules, Chaing Mai J. Sci. 33 (2006), no. 1, 3-7.

5.
S. Ebrahimi Atani and R. Ebrahimi Atani, Graded multiplication modules and the graded ideal ${\theta}_g(M)$, Turk. J. Math. 33 (2009), 1-9.

6.
S. Ebrahimi Atani and F. Farzalipour, On graded multiplication modules, Chiang Mai J. Sci., To appear.

7.
S. Ebrahimi Atani and A. Yousefian Darani, Graded primal ideals, Georgian Math. J., Ahead of print.

8.
L. Fuchs, On primal ideals, Proc. Amer. Math. Soc. 1 (1950), 1-6.

9.
J. A. Huckaba, Commutative Rings with Zero-Divisors, monographs and textbooks in Pure and Applied mathematics, 117, Marcel Dekker, Inc., Now York, 1988.

10.
C. Nastasescu and F. Oystaeyen, Methods of Graded Rings, Lecture Notes in Mathematics, 1836. Springer-Verlag, Berlin, 2004.

11.
M. Refai and K. Al-Zoubi, On Graded Primary Ideals, Turkish J. Math. 28 (2004), no. 3, 217-229.

12.
R. Y. Sharp, Asymptotic behaviour of certain sets of attached prime ideals, J. London Math. Soc. (2) 34 (1986), no. 2, 212-218.

13.
P. Smith, Some remarks on multiplication modules, Arch. Math. 50 (1988), no. 3, 223-235.