Stone Duality on P-Rings

摘要

For given p (= prime), a p-ring as first introduced by Mc Coy and Montgomery [2]. The concept of p-ring is an evident generalization of that of Boolean ring (p = 2). The well known result of Stone [7], each Boolean ring is isomorphically representable as a ring of classes or what is equivalent, is isomorphic with a sub ring of some direct power of Z_(2) ( 2-element Boolean ring = field of residues mod 2) was generalized by Mc Coy and Montgomery [2] to: each p-ring is a isomorphic with a sub ring of some direct power of Z_(P) (field of residues mod p) and they showed that each finite p-ring is isomorphic with a sub ring of some direct power of Z_(P). The present communication concerned with a further study of p-rings. In particular we study the topological properties of p-rings and proved a Stone duality theorem.