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Dergiler / International Electronic Journal of Algebra / 2017 / Cilt: 21 - Sayı: 21

EXTENSIONS OF Σ-ZIP RINGS

Ouyang LUNQUN
Zhou QİONG
Wu JİNFANG
Sayfa
1–22
Yayın Tarihi
2017-01-17
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

As a consequence, we obtain a generalization of several known results relating to zip rings and weak zip rings.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this note we consider a new concept, so called Σ-zip ring, which unifies zip rings and weak zip rings.
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Temel Bulgular & Veri:We observe the basic properties of Σ-zip rings, constructing typical examples.
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Sonuç & Katkı:As a consequence, we obtain a generalization of several known results relating to zip rings and weak zip rings.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Σ-zip ring · Ore extension

Abstract

t. In this note we consider a new concept, so called Σ-zip ring, which unifies zip rings and weak zip rings. We observe the basic properties of Σ-zip rings, constructing typical examples. We study the relationship between the Σ-zip property of a ring R and that of its Ore extensions and skew generalized power series extensions. As a consequence, we obtain a generalization of several known results relating to zip rings and weak zip rings.

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Bu Makaleye Atıf Yap

LUNQUN, O., QİONG, Z., JİNFANG, W. (2017). EXTENSIONS OF Σ-ZIP RINGS. International Electronic Journal of Algebra, Cilt: 21 - Sayı: 21, 1–22. https://ajindex.com/articles/832355

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Kaynakça (1)

  1. E. Hashemi and A. Moussavi, Polynomial extensions of quasi-Baer rings, Acta Math. Hungar., 107(3) (2005), 207-224. [6] C. Y. Hong, N. K. Kim, T. K. Kwak and Y. Lee, Extensions of zip rings, J. Pure Appl. Algebra, 195(3) (2005), 231-242. [7] Z. K. Liu, Triangular matrix representations of rings of generalized power series, Acta Math. Sin. (Engl. Ser.), 22(4) (2006), 989-998. [8] G. Marks, On 2-primal Ore extensions, Comm. Algebra, 29(5) (2001), 2113- 2123. [9] R. Mazurek and M. Ziembowski, Uniserial rings of skew generalized power series, J. Algebra, 318(2) (2007), 737-764 [10] L. Ouyang, Ore extensions of weak zip rings, Glasg. Math. J., 51(3) (2009), 525-537. [11] M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci., 73(1) (1997), 14-17. [12] P. Ribenboim, Rings of generalized power series: Nilpotent elements, Abh. Math. Sem. Univ. Hamburg, 61 (1991), 15-33. [13] P. Ribenboim, Noetherian rings of generalized power series, J. Pure Appl. Algebra, 79(3) (1992), 293-312. [14] J. M. Zelmanowitz, The finite intersection property on annihilator right ideals, Proc. Amer. Math. Soc., 57(2) (1976), 213-216.