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Let σ be an endomorphism and I a σ-ideal of a ring R. Pearson and Stephenson called I a σ-semiprime ideal if whenever A is an ideal of R and m is an integer such that Aσt(A) ⊆ I for all t ≥ m, then A ⊆ I,where σ is an automorphism, and Hong et al. called I a σ-rigid ideal if aσ(a) ∈ I implies a ∈ I for a ∈ R. Notice that R is called a σ-semiprime ring (resp., a σ-rigid ring) if the zero ideal of R is a σ-semiprime ideal (resp., a σ-rigid ideal). Every σ-rigid ideal is a σ-semiprime ideal for an automorphism σ, but the converse does not hold, in general. We, in this paper, introduce the quasi σ-rigidness of ideals and rings for an automorphism σ which is in between the σ-rigidness and the σ-semiprimeness,and study their related properties. A number of connections between the quasi σ-rigidness of a ring R and one of the Ore extension R[x; σ, δ] of R are also investigated. In particular, R is a (principally) quasi-Baer ring if and only if R[x; σ, δ] is a (principally) quasi-Baer ring, when R is a quasi σ-rigid ring.
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참고문헌 (22)
참고문헌 신청
A. A. M. Kamal / 1994 / Some remarks on Ore extension rings / Comm. Algebra 22 (10) : 3637 ~ 3667
C. Y. Hong / 2000 / On minimal strongly prime ideals / Comm. Algebra 28 (10) : 4867 ~ 4878
C. Y. Hong / 2000 / Ore extensions of Baer and p.p.-rings / J. Pure Appl. Algebra 151 (3) : 215 ~ 226
C. Y. Hong / 2003 / On skew Armendariz rings / Comm. Algebra 31 (1) : 103 ~ 122
C. Y. Hong / 2005 / Rigid ideals and radicals of Ore extensions / Algebra Colloq. 12 (3) : 399 ~ 412
C. Y. Hong / 2000 / On minimal strongly prime ideals / Comm. Algebra 28 (10) : 4867 ~ 4878
C. Y. Hong / 2000 / Ore extensions of Baer and p.p.-rings / J. Pure Appl. Algebra 151 (3) : 215 ~ 226
C. Y. Hong / 2003 / On skew Armendariz rings / Comm. Algebra 31 (1) : 103 ~ 122
C. Y. Hong / 2005 / Rigid ideals and radicals of Ore extensions / Algebra Colloq. 12 (3) : 399 ~ 412
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