ON PRIME SUBMODULES AND PRIMARY DECOMPOSITIONS IN TWO-GENERATED FREE MODULES
TAIWANESE JOURNAL OF MATHEMATICS, cilt.17, sa.1, ss.133-142, 2013 (SCI-Expanded)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 17 Sayı: 1
- Basım Tarihi: 2013
- Doi Numarası: 10.11650/tjm.17.2013.1803
- Dergi Adı: TAIWANESE JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.133-142
- Anahtar Kelimeler: Prime submodule, Primary submodule, Primary decomposition
- Akdeniz Üniversitesi Adresli: Evet
Özet
In this paper, we consider the free R-module R circle plus R, where R is an arbitrary commutative ring with identity. We give a full characterization for prime submodules of R circle plus R and a useful primeness test for a finitely generated submodule of R circle plus R. We study the existence of primary decomposition of a submodule of R circle plus R and characterize the minimal primary decomposition. As applications of our results, we give some examples of primary decompositions in R circle plus R.