αcc-Baer rings, α-Baer rings, αcc-disconnected, αcc-Baer hull, Baer-rings, f-rings
Let α denote an infinite cardinal or ∞ which is used to signify no cardinal constraint. This work introduces the concept of an αcc-Baer ring and demonstrates that a commutative semiprime ring A with identity is αcc-Baer if and only if Spec(A) is αcc-disconnected. Moreover, we prove that for each commutative semprime ring A with identity there exists a minimum αcc-Baer ring of quotients, which we call the αcc-Baer hull of A. In addition, we investigate a variety of classical α-Baer ring results within the contexts of αcc-Baer rings and apply our results to produce alternative proofs of some classical results such as A is α-Baer if and only if Spec(A) is α-disconnected. Lastly, we apply our results within the contexts of archimedean f-rings.
Carrera, Ricardo Enrique; Iberkleid, Wolf; Lafuente-Rodriguez, Ramiro; and McGovern, Warren William, "αcc-Baer Rings" (2015). Mathematics Faculty Articles. 215.