Idempotent-prime ideals and Baer-type rings with involution

Abstract

In this article, we study some idempotent-structures as $\mathfrak{c}\mathfrak{P}$-Baer rings and $\mathcal{I}$-prime rings. Moreover, we define $\mathfrak{c}\mathfrak{P}$-Baer *-rings and $\mathcal{I}$-*-prime *-rings as involutive versions of $\mathfrak{c}\mathfrak{P}$-Baer rings and $\mathrm{I}$-prime rings and expose their properties. Furthermore, the relation between these rings and those without involution are indicated. Finally, some extensions for $\mathfrak{c}\mathfrak{P}$-Baer *-rings are given, for instance the polynomial ring $R[x]$ is a $\mathfrak{c}\mathfrak{P}$-Baer *-ring if and only if R is a $\mathfrak{c}\mathfrak{P}$-Baer *-ring.

Keywords:

• $\mathfrak{c}\mathfrak{P}$-Baer
• *-central reduced
• Involution
• $\mathcal{I}$-prime

2020 Mathematics Subject Classification:

• 16D25
• 16N60
• 16W10
• 16U40
• 13C10
• 16S70