Abstract
The study of prime ideals has been an active area of research and a considerable work has been done in this direction during recent past. Associated prime ideals and minimal prime ideals of certain types of Ore extensions have been characterized.
We recall that a right ideal I of a ring R is called a prime right ideal if JK ⊆ I for some right ideals J, K of R such that JI ⊆ I, then either J ⊆ I or K ⊆ I. Also a right ideal P of R is said to be completely prime right ideal if for any a, b ∈ R such that aP ⊆ P, ab ∈ P implies that a ∈ P or b ∈ P.
In this paper we discuss the left analogue of these notions and give a relation between completely prime left ideals of a ring R and those of R[x; σ, δ]; where σ is an automorphisms of R and δ a σ-derivation of R. It has been proved that if P is a completely prime left ideal of R such that σ(P) = P and δ(P) ⊆ P, then P[x; σ, δ] is a completely prime left ideal of R[x; σ, δ].
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Bhat, V.K. On completely prime left ideals of Ore extensions. Lobachevskii J Math 36, 79–84 (2015). https://doi.org/10.1134/S1995080215010047
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DOI: https://doi.org/10.1134/S1995080215010047