Nilpotent Elements in Skew Polynomial Rings

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AZIMI M.; MOUSSAVI A.

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Paper Information

Journal: JOURNAL OF SCIENCES, ISLAMIC REPUBLIC OF IRAN Year:2017 | Volume:28 | Issue:1 Page(s): 59-74

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Title

Nilpotent Elements in Skew Polynomial Rings

Author(s)

AZIMI M. | MOUSSAVI A. | Issue Writer Certificate

Keywords

(



) 

compatible ring

Skew polynomial ring

Skew power series ring

Abstract

Let R be a ring with an endomorphism  and an -derivation . Antoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil-( ,  )-compatible rings. The class of nil-( ,  )-compatible rings are extended through various ring extensions and many classes of nil-( ,  )-compatible rings are constructed. We also prove that, if R is nil--compatible and nil-Armendariz ring of power series type with nil  R  nilpotent, then nil(R[[x;  ]])  nil(R)[[x;  ]]. We show that, if R is a nil-Armendariz ring of power series type, with nil  R  nilpotent and nil-( ,  )-compatible ring, then nil  R  x;  ,     nil  R   x;  ,   . As a consequence, several known results are unified and extended to the more general setting. Also examples are provided to illustrate our results.

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APA: Copy

AZIMI, M., & MOUSSAVI, A.. (2017). Nilpotent Elements in Skew Polynomial Rings. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, 28(1), 59-74. SID. https://sid.ir/paper/718836/en

Vancouver: Copy

AZIMI M., MOUSSAVI A.. Nilpotent Elements in Skew Polynomial Rings. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN[Internet]. 2017;28(1):59-74. Available from: https://sid.ir/paper/718836/en

IEEE: Copy

M. AZIMI, and A. MOUSSAVI, “Nilpotent Elements in Skew Polynomial Rings,” JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, vol. 28, no. 1, pp. 59–74, 2017, [Online]. Available: https://sid.ir/paper/718836/en

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