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Dergiler / International Electronic Journal of Algebra / 2026 / Volume: 1 Issue: 1

ON SEMIPERFECT F-INJECTIVE RINGS

Truong Cong Quynh
Sayfa
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Yayın Tarihi
2007-06-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Some known results are obtained as corollaries.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:A ring R is called right F-injective if every right R-homomorphism from a finitely generated right ideal of R to R extends to an endomorphism of R.
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Temel Bulgular & Veri:We prove that if R is left perfect, right F-injective, then R is QF if and only if R/S is left finitely cogenerated where S = Sr = Sl if and only if R is left semiartinian, Soc2(R) is left finitely generated.
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Sonuç & Katkı:Some known results are obtained as corollaries.
🔬Tür:Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:F(P)-injective ring · mininjective ring · finitely continuous ring

Abstract

A ring R is called right F-injective if every right R-homomorphism from a finitely generated right ideal of R to R extends to an endomorphism of R. R is called a right FSE-ring if R is a right F-injective semiperfect ring with essential right socle. The class of right FSE-rings is broader than that of right PF-rings. In this paper, we study and provide some characterizations of this class of rings. We prove that if R is left perfect, right F-injective, then R is QF if and only if R/S is left finitely cogenerated where S = Sr = Sl if and only if R is left semiartinian, Soc2(R) is left finitely generated. It is also proved that R is QF if and only if R is left perfect, mininjective and J2 = r(I) for a finite subset I of R. Some known results are obtained as corollaries.

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Bu Makaleye Atıf Yap

Quynh, T. C. (2007). ON SEMIPERFECT F-INJECTIVE RINGS. International Electronic Journal of Algebra, Volume: 1 Issue: 1. https://ajindex.com/articles/1588378

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