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Journal of Mathematics
Volume 2017 (2017), Article ID 3817479, 8 pages
Research Article

Properties of -Primal Graded Ideals

Department of Mathematics, The Hashemite University, Zarqa 13115, Jordan

Correspondence should be addressed to Ameer Jaber

Received 28 February 2017; Revised 28 April 2017; Accepted 11 May 2017; Published 4 June 2017

Academic Editor: Naihuan Jing

Copyright © 2017 Ameer Jaber. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let be a commutative graded ring with unity . A proper graded ideal of is a graded ideal of such that . Let be any function, where denotes the set of all proper graded ideals of . A homogeneous element is -prime to if where is a homogeneous element in ; then . An element is -prime to if at least one component of is -prime to . Therefore, is not -prime to if each component of is not -prime to . We denote by the set of all elements in that are not -prime to . We define to be -primal if the set (if ) or (if ) forms a graded ideal of . In the work by Jaber, 2016, the author studied the generalization of primal superideals over a commutative super-ring with unity. In this paper we generalize the work by Jaber, 2016, to the graded case and we study more properties about this generalization.