Effective ring

B. V. Zabavsky, B. M. Kuznitska

Abstract


In this paper we will investigate commutative Bezout domains whose finite homomorphic images are semipotent rings. Among such commutative Bezout rings we consider a new class of rings and call them an effective rings. Furthermore we prove that effective rings are elementary divisor rings.


Keywords


Bezout ring, exchange ring, clean ring, effective ring, elementary divisor ring, idempotent of stable range 1, neat ring

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