Let G be a group and R G-graded ring. In this paper, we present examine the concept of graded weakly 2-absorbing ideals as in generality prime ring which is not commutative, demonstrates that symmetry obtained lot outcomes commutative rings remain are commutative.

One of the most general extensions of Buchberger's theory of Grobner bases is the concept of graded structures due to Robbiano and Mora. But in order to obtain algorithmic solutions for the computation of Gr obner bases it needs additional computability assumptions. In this paper we introduce natural graded structures of nitely generated extension rings and present subclasses of such structur...

In this paper, we introduce and study graded weakly 1-absorbing prime ideals in commutative rings. Let \(G\) be a group \(R\) \(G\)-graded ring with nonzero identity \(1\neq0\). A proper ideal \(P\) of is called if for each nonunits \(x,y,z\in h(R)\) \(0\neq xyz\in P\), then either \(xy\in P\) or \(z\in P\). We give many properties characterizations ideals. Moreover, investigate under homomorph...

If A is a strongly noetherian graded algebra generated in degree one, then there is a canonically constructed graded ring homomorphism from A to a twisted homogeneous coordinate ring B(X,L, σ), which is surjective in large degree. This result is a key step in the study of projectively simple rings. The proof relies on some results concerning the growth of graded rings which are of independent i...

If A is a strongly noetherian graded algebra generated in degree one, then there is a canonically constructed graded ring homomorphism from A to a twisted homogeneous coordinate ring B(X,L, σ), which is surjective in large degree. This result is a key step in the study of projectively simple rings. The proof relies on some results concerning the growth of graded rings which are of independent i...