Ricardo Enrique CarreraIberkleidLafuente-RodriguezWarren Wm. McGovern2026-03-222026-03-22201510.1515/ms-2015-0029https://doi.org/10.1515/ms-2015-0029https://andeanlibrary.org/handle/123456789/63242Abstract 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.enMathematicsSemiprime ringRing (chemistry)Noncommutative ringCommutative ringIdentity (music)Pure mathematicsQuotientReduced ringMathematical proofarticle