Graded 1-absorbing prime ideals of graded commutative rings. (English) Zbl 1535.13006
Summary: Let \(G\) be a group with identity \(e\) and \(R\) be \(G\)-graded commutative ring with \(1\neq 0\). In this paper, we introduce and study the graded versions of 1-absorbing prime ideal. We give some properties and characterizations of these ideals in graded ring, and we give a characterization of graded 1-absorbing ideal the idealization \(R(+)M\).
MSC:
| 13A15 | Ideals and multiplicative ideal theory in commutative rings |
| 13A02 | Graded rings |
| 13C05 | Structure, classification theorems for modules and ideals in commutative rings |
| 13H05 | Regular local rings |
Keywords:
graded ring; graded ideals; graded prime ideal; trivial ring extensions; graded modules; graded submodulesReferences:
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