Rings of Morita contexts which are maximal orders
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.15, no.7, 2016 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 15 Issue: 7
- Publication Date: 2016
- Doi Number: 10.1142/s0219498816501292
- Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Hacettepe University Affiliated: Yes
Abstract
Let T = (R W V S) be a ring of Morita context which is a prime Goldie ring with its quotient ring (Q(R) Q(W) Q(V) Q(S)). We define the notion of an (R, S)-maximal module in Q(V) and that of an (S, R)-maximal module in Q(W) from order theoretical point of view and give some necessary and sufficient conditions for T to be a maximal order in terms of (R, S)-module V and (S, R)-module W. In case T is a maximal order, we explicitly describe the structure of v-T-ideals. These results are applied to obtain necessary and sufficient conditions for T to be an Asano order or a Dedekind order.