BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS

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HASHEMI E.; KHALILNEZHAD KH.; GHADIRI HERATI M.

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ISSN: 2588-4824

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Journal: JOURNAL OF ALGEBRAIC SYSTEMS Year:2019 | Volume:7 | Issue:1 Page(s): 1-24

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Title

BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS

Author(s)

HASHEMI E. | KHALILNEZHAD KH. | GHADIRI HERATI M. | Issue Writer Certificate

Keywords

quasi

Baer rings

quasi

Baer rings

skew PBW extensions

Abstract

A ring R with an automorphism and a -derivation is called -quasi-Baer (resp., -invariant quasi-Baer) if the right annihilator of every -ideal (resp., -invariant ideal) of R is generated by an idempotent, as a right ideal. In this paper, we study Baer and quasi-Baer properties of skew PBW extensions. More exactly, let A = (R) ⟨ x1; : : :; xn⟩ be a skew PBW extension of derivation type of a ring R. (i) It is shown that R is Δ-quasi-Baer if and only if A is quasi-Baer. (ii) R is Δ-Baer if and only if A is Baer, when R has IFP. Also, let A = (R) ⟨ x1; : : :; xn⟩ be a quasi-commutative skew PBW extension of a ring R. (iii) If R is a -quasi-Baer ring, then A is a quasi-Baer ring. (iv) If A is a quasi-Baer ring, then R is a -invariant quasi-Baer ring. (v) If R is a -Baer ring, then A is a Baer ring, when R has IFP. (vi) If A is a Baer ring, then R is a -invariant Baer ring. Finally, we show that if A = (R) ⟨ x1; : : :; xn⟩ is a bijective skew PBW extension of a quasi-Baer ring R, then A is a quasi-Baer ring.

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APA: Copy

HASHEMI, E., KHALILNEZHAD, KH., & GHADIRI HERATI, M.. (2019). BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS. JOURNAL OF ALGEBRAIC SYSTEMS, 7(1 ), 1-24. SID. https://sid.ir/paper/268350/en

Vancouver: Copy

HASHEMI E., KHALILNEZHAD KH., GHADIRI HERATI M.. BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS. JOURNAL OF ALGEBRAIC SYSTEMS[Internet]. 2019;7(1 ):1-24. Available from: https://sid.ir/paper/268350/en

IEEE: Copy

E. HASHEMI, KH. KHALILNEZHAD, and M. GHADIRI HERATI, “BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS,” JOURNAL OF ALGEBRAIC SYSTEMS, vol. 7, no. 1 , pp. 1–24, 2019, [Online]. Available: https://sid.ir/paper/268350/en

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