On essential extensions of direct sums of either injective or projective modules

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Kosan M. T., Truong Cong Quynh T. C. Q.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.13, sa.7, 2014 (SCI-Expanded, Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 13 Sayı: 7
• Basım Tarihi: 2014
• Doi Numarası: 10.1142/s0219498814500388
• Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Gazi Üniversitesi Adresli: Hayır

Özet

For a ring R, there are classical facts that R is right Noetherian if and only if every direct sum of injective right R-modules is injective, and R is right Noetherian if and only if every essential extension of a direct sum of injective hulls of simple right R-modules is a direct sum of injective right R-modules. In this paper, we prove that R is right Noetherian if and only if every essential extension of a direct sum of injective hulls of simple right R-modules is a direct sum of either injective right R-modules or projective right R-modules.