$α$cc-Baer rings

Rok, strany: 2015, 371 - 386

Let $α$ denote an infinite cardinal or $∞$ which is used to signify no cardinal constraint. This work introduces the concept of an $α$cc-Baer ring and demonstrates that a commutative semiprime ring $A$ with identity is $α$cc-Baer if and only if $\Spec(A)$ is $α$cc-disconnected. Moreover, we prove that for each commutative semprime ring $A$ with identity there exists a minimum $α$cc-Baer ring of quotients, which we call the $α$cc-Baer hull of $A$. In addition, we investigate a variety of classical $α$-Baer ring results within the contexts of $α$cc-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.

ISO 690:

Carrera, R., Iberkleid, ., Lafuente-Rodriguez, ., Mcgovern, W. 2015. $α$cc-Baer rings. In Mathematica Slovaca, vol. 65, no.2, pp. 371-386. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0029

APA:

Carrera, R., Iberkleid, ., Lafuente-Rodriguez, ., Mcgovern, W. (2015). $α$cc-Baer rings. Mathematica Slovaca, 65(2), 371-386. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0029