Titlebook: Advances in Rings, Modules and Factorizations; Graz, Austria, Febru Alberto Facchini,Marco Fontana,Bruce Olberding Conference proceedings 2

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Valuative Marot Rings,are weakly valuative rings that are not valuative, and valuative rings that are not strongly valuative. In the special case that . is a Marot ring (each regular ideal can be generated by a set of regular elements), . is weakly valuative if and only if it is strongly valuative. Also a valuative Marot ring has at most three regular maximal ideals.

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Studies in Computational IntelligenceWe prove a Bazzoni-type theorem for multiplicative lattices thus unifying several ring/monoid theoretic results of this type.

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https://doi.org/10.1007/978-90-481-3575-2We present a dimension theory for modules in ., where . is a class of modules with semilocal endomorphism rings satisfying certain smallness conditions. For example, if . is the class of all finitely presented modules over a semilocal ring ., then we get cardinal invariants which describe pure projective .-modules up?to isomorphism.

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