Abstract
Let G be a group with identity e and let R be a commutative G-graded ring. In this paper, we will investigate commutative graded rings which satisfy the condition \((*)\). We say that a graded ring R satisfy the condition \((*)\) if P is a graded prime ideal of R and if \(\{I_{\alpha }\}_{\alpha \in \Delta }\) is a family of graded ideals of R, then P contains \(\cap _{\alpha \in \Delta }I_{\alpha }\) only if P contains some \(I_{\alpha }\).
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Al-Zoubi, K., Qarqaz, F. An intersection condition for graded prime ideals. Boll Unione Mat Ital 11, 483–488 (2018). https://doi.org/10.1007/s40574-017-0148-7
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DOI: https://doi.org/10.1007/s40574-017-0148-7