RESEARCH ARTICLE

Effective ring

B. V. Zabavsky, B. M. Kuznitska

Department of Mechanics and Mathematics, Ivan Franko National Univ., Lviv, Ukraine

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.

MSC: 13F99

Received: 04.01.2014
Revised: 26.07.2014

Language: English

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