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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2009 / Cilt: 58 - Sayı: 1

ON REDUCED MODULES

N. AGAYEV
S. HALICIOĞLU
A. HARMANCI
Pages
9–16
Publication Date
2009-02-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Among others we prove that a ring R is α- reduced if and only if every áat right R-module is -reduced, and for a module M, M[x] is α-reduced if and only if M[x; x1 ] is α-reduced.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let α be an endomorphism of an arbitrary ring R with identity.
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Key Findings & Data:In this note, we concern the relations between polynomial and power series extensions of a reduced module.
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Conclusion & Impact:Among others we prove that a ring R is α- reduced if and only if every áat right R-module is -reduced, and for a module M, M[x] is α-reduced if and only if M[x; x1 ] is α-reduced.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:reduced modules

Abstract

Abstract. Let α be an endomorphism of an arbitrary ring R with identity. In this note, we concern the relations between polynomial and power series extensions of a reduced module. Among others we prove that a ring R is α- reduced if and only if every áat right R-module is -reduced, and for a module M, M[x] is α-reduced if and only if M[x; x1 ] is α-reduced.

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Cite This Article

AGAYEV, N., HALICIOĞLU, S., HARMANCI, A. (2009). ON REDUCED MODULES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 58 - Sayı: 1, 9–16. https://ajindex.com/articles/747469

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References (6)

  1. N. Agayev and A. Harmanci, On semicommutative modules and rings, Kyungpook Math. J., 47(2007)(1), 21-30.
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  3. A.M. Buhphang and M.B. Rege, Semi-commutative module and Armendariz modules, Arab. J. Math. Sci., (8) (2002), 53-65.
  4. W.X. Chen and W.T. Tong, A note on skew Armendariz rings, Com. Algebra, 33 (2005), 1137-1140.
  5. C.Y. Hong, N.K. Kim and T.K. Kwak, Ore extensions of Baer and p.p.-rings, J. Pure and Appl. Algebra, 151 (3)(2000), 215-226.
  6. T.K. Lee and Y. Zhou, Reduced modules, Rings, modules, algebras, and abelian groups, 365– 377, Lecture Notes in Pure and Appl. Math., 236, Dekker, New York, 2004. C. Zhang and J. Chen, skew Armendariz modules and semicommu- tative modules, Tai wanese J. Math., 12 (2) (2008), 473-486. Current address:, N. Agayev: Department of Pedagogy, Qafqaz University, Baku, Azerbaijan S. Halıcıo¼glu: Department of Mathematics, Ankara University, Ankara, Turkey A.Harmanci: Department of Mathematics,Hacettepe University, Ankara, Turkey E-mail address: [email protected], [email protected] [email protected]