Arithmetic Rings and their generalizations

  • R. Strano Dipartimento di Matematica e Informatica, Università di Catania, Italy
Keywords: commutative rings, ideals, domains


Prüfer domains are characterized by various properties regarding ideals and operations between them. In this note we consider six of these properties. The natural generalization of the notion of Prüfer domain to the case of a commutative ring with unit, not necessarily a domain, is the notion of arithmetic ring. We ask if the previous properties characterize arithmetic ring in the case of a general commutative ring with unit. We prove that four of such properties characterize arithmetic rings while the remaining two are weaker and give rise to two different generalizations.

How to Cite
Strano, R. (2018). Arithmetic Rings and their generalizations. Bullettin of the Gioenia Academy of Natural Sciences of Catania, 51(381), FP1-FP6.
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