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Graded 1-Absorbing Prime Ideals over Non-Commutative Graded Rings
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In this article, we define and study graded 1-absorbing prime ideals and graded weakly 1-absorbing prime ideals in non-commutative graded rings as a new class of graded ideals that lies between graded prime ideals (graded weakly prime ideals) and graded 2-absorbing ideals (graded weakly 2-absorbing ideals). Let G be a group and let R be a non-commutative G-graded ring with nonzero unity. Let P be a proper graded ideal of R. We then say that P is a graded 1-absorbing prime ideal (a graded weakly 1-absorbing prime ideal) of R if, for each nonunit homogeneous element r,s,t∈R with rRsRt⊆P ({0}≠rRsRt⊆P), either rs∈P or t∈P. We present a number of properties and characterizations of these graded ideals.
Title: Graded 1-Absorbing Prime Ideals over Non-Commutative Graded Rings
Description:
In this article, we define and study graded 1-absorbing prime ideals and graded weakly 1-absorbing prime ideals in non-commutative graded rings as a new class of graded ideals that lies between graded prime ideals (graded weakly prime ideals) and graded 2-absorbing ideals (graded weakly 2-absorbing ideals).
Let G be a group and let R be a non-commutative G-graded ring with nonzero unity.
Let P be a proper graded ideal of R.
We then say that P is a graded 1-absorbing prime ideal (a graded weakly 1-absorbing prime ideal) of R if, for each nonunit homogeneous element r,s,t∈R with rRsRt⊆P ({0}≠rRsRt⊆P), either rs∈P or t∈P.
We present a number of properties and characterizations of these graded ideals.
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