Rings of Morita contexts which are maximal orders


SARAÇ B. , AKALAN E. , AYDOĞDU P. , MARUBAYASHI H.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.15, sa.7, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Konu: 7
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1142/s0219498816501292
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS

Özet

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.