MODULES WHOSE CERTAIN SUBMODULES ARE ESSENTIALLY EMBEDDED IN DIRECT SUMMANDS
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, cilt.46, sa.2, ss.519-532, 2016 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 46 Sayı: 2
- Basım Tarihi: 2016
- Doi Numarası: 10.1216/rmj-2016-46-2-519
- Dergi Adı: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.519-532
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Hacettepe Üniversitesi Adresli: Evet
Özet
It is well known that, if the ring has acc on essential right ideals, then for every quasi-continuous module over the ring, the finite exchange property implies the full exchange property. In this paper, we obtain the former implication for the generalizations of quasi-continuous modules over a ring with acc on right annhilators of elements of the module. Moreover, we focus on direct sums and direct summands of weak C-12 modules i.e., modules with the property that every semisimple submodule can be essentially embedded in a direct summand. To this end, we prove that since weak C-12 is closed under direct sums. Amongst other results, we provide several counterexamples including the tangent bundle of a real sphere of odd dimension over its coordinate ring for the open problem of whether weak C-12 implies the C-12 condition.