Titlebook: Rings, Monoids and Module Theory; AUS-ICMS 2020, Sharj Ayman Badawi,Jim Coykendall Conference proceedings 2021 The Editor(s) (if applicable

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,Tame-Wild Dichotomy for Commutative Noetherian Rings—A Survey,ings do these categories have wild representation type?” We also address the question: “Can a Noetherian ring have both tame and wild representation type?” We provide an outline for showing that many tame rings are not wild.

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Bounded and Finite Factorization Domains, domain if it is atomic and for every nonzero nonunit ., there is a positive integer . such that for any factorization . of . into irreducibles . in ., the inequality . holds. In addition, we say that . is a finite factorization domain if it is atomic and every nonzero nonunit in . factors into irre

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Factorization and Irreducibility in Modules,sors. In this chapter we study module-theoretic generalizations of some notions they studied. Our focus is on formulating appropriate definitions of the various kinds of “irreducibility” and “atomicity.” We study the consequences of these definitions and investigate to what extent ring-theoretic res

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On ,-potent Domains and ,-homogeneous Ideals, maximal .-ideal that contains a .-homogeneous ideal is called potent and the same name bears a domain all of whose maximal .-ideals are potent. One among the various aims of this article is to indicate what makes a .-ideal of finite type a .-homogeneous ideal, where and how we can find one, what th

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