Shahabaddin Ebrahimi ATANİ

On Graded Weakly Prime Ideals

Let G be an arbitrary group with identity e, and let R be a G-graded commutative ring. Weakly prime ideals in a commutative ring with non-zero identity have been introduced and studied in [1]. Here we study the graded weakly prime ideals of a G-graded commutative ring. A number of results concerning graded weakly prime ideals are given. For example, we give some characterizations of graded weakly prime ideals and their homogeneous components.

Anahtar Kelimeler:

Graded rings, Graded weakly prime ideals

On Graded Weakly Prime Ideals

Keywords:

Graded rings, Graded weakly prime ideals,

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[1] Anderson, D. D. and Smith, E.: Weakly prime ideals, Houston J. of Mathematics, 29, 831-840, (2003).
[2] Ebrahimi Atani, S. and Farzalipour, F.: On weakly primary ideals, Georgian Mathematical Journal, 12, 423-429, (2005).
[3] Nastasescu, C. and Van Oystaeyen, F.: Graded Ring Theory, Mathematical Library 28, North Holand, Amsterdam, (1982).
[4] Refai M. and Al-Zoubi, K.: On Graded Primary Ideals, Turkish Journal of Mathematics, 28, 217-229, (2004).