Ideal Structure of Leavitt Path Algebras with Coefficients in a Unital Commutative Ring |
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Authors: | Hossein Larki |
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Institution: | 1. Department of Mathematics, Faculty of Mathematical Sciences and Computer , Shahid Chamran University , Ahvaz , Iran h.larki@scu.ac.ir |
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Abstract: | For a (countable) graph E and a unital commutative ring R, we analyze the ideal structure of the Leavitt path algebra L R (E) introduced by Mark Tomforde. We first modify the definition of basic ideals and then develop the ideal characterization of Mark Tomforde. We also give necessary and sufficient conditions for the primeness and the primitivity of L R (E), and we then determine prime graded basic ideals and left (or right) primitive graded ideals of L R (E). In particular, when E satisfies Condition (K) and R is a field, they imply that the set of prime ideals and the set of primitive ideals of L R (E) coincide. |
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Keywords: | Graded ideal Leavitt path algebra Prime ideal Primitive ideal ?-graded ring |
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