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Journal of Mathematical Sciences, 2005
The Jacobson density theorem states that any primitive ring is a dense subring of the ring of linear transformations of a vector space over some division ring. The paper provides three graded versions of the density theorem for the rings graded by semigroups and modules graded by acts over these semigroups with additional cancellation conditions.
Balaba, I. N. +3 more
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Artinian Semigroup-Graded Rings

Bulletin of the London Mathematical Society, 1995
Let $S$ be a semigroup with no infinite subgroups and let $R$ be a right Artinian $S$-graded ring. We prove that $R$ necessarily has finite support.
Clase, M. V. +3 more
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A Class of Band-Graded Rings

Journal of the London Mathematical Society, 1992
A ring means an associative ring. Let $S$ be a semigroup. A ring $R$ is $S$-graded iff $R=\oplus R_ x$ $(x\in S)$, where $R_ x$ is a subring of $R$ and $R_ xR_ y\subset R_{xy}$ for all $x,y\in S$. Let $\Omega$ be a band (i.e. $\Omega$ is a semigroup consisting of idempotents only), and let $R$ be a ring graded by $\Omega$. The
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Ring theoretical properties of epsilon-strongly graded rings and Leavitt path algebras

Communications in Algebra, 2022
Luis Martinez, Hector Pinedo
exaly

Idempotents in a Graded Ring

Journal of the London Mathematical Society, 1974
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Methods of Graded Rings