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Chain Conditions for Epsilon-Strongly Graded Rings with Applications to Leavitt Path Algebras
Let G be a group with neutral element e and let $S=\bigoplus _{g \in G}S_{g}$ be a G-graded ring. A necessary condition for S to be noetherian is that the principal component Se is noetherian. The following partial converse is well-known: If S is strongly-graded and G is a polycyclic-by-finite …