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

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A Survey on the Local Invertibility of Ideals in Commutative Rings,Let . be an integral domain. We give an overview on connections between the (.)-finite character property of . (i.e., each nonzero element of . is contained in finitely many (.)-maximal ideals) and problems of local invertibility of ideals.

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,Idempotence and Divisoriality in Prüfer-Like Domains,Let . be a Prüfer .-multiplication domain, where . is a semistar operation on .. We show that certain ideal-theoretic properties related to idempotence and divisoriality hold in Prüfer domains, and we use the associated semistar Nagata ring of . to show that the natural counterparts of these properties also hold in ..

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Classifying Modules in Add of a Class of Modules with Semilocal Endomorphism Rings,We 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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,When Two Principal Star Operations Are the Same,We study when two fractional ideals of the same integral domain generate the same star operation.

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https://doi.org/10.1007/978-3-030-43416-8multiplicative ideal theory; integer-valued polynomial; monoid; factorization; commutative ring; Prufer r

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978-3-030-43418-2Springer Nature Switzerland AG 2020