Occasioned by the international conference "Rings and Factorizations" held in February 2018 at University of Graz, Austria, this volume represents a wide range of research trends in the theory of commutative and non-commutative rings and their modules, including multiplicative ideal theory, Dedekind and Krull rings and their generalizations, rings of integer valued-polynomials, topological aspects of ring theory, factorization theory in rings and semigroups and direct-sum decompositions of modules. The volume will be of interest to researchers seeking to extend or utilize work in these areas as well as graduate students wishing to find entryways into active areas of current research in algebra. A novel aspect of the volume is an emphasis on how diverse types of algebraic structures and contexts (rings, modules, semigroups, categories) may be treated with overlapping and reinforcing approaches.
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Anh, P. N., Kearnes, K., and Szendrei, A: Commutative Rings Whose Principal Ideals Have Unique Generators.- Brantner, J., Geroldinger, A., and Reinhart, A: On monoids of ideals of orders in quadratic number fields.- Chang, G. W.: UMT-domains: A survey.- D'Anna, M., Guerrieri, L., and Micale, V: The Ap ´ery Set of a Good Semigroup.- Domokos, M.: On syzygies for rings of invariants of abelian groups.- Dumitrescu, T.: A Bazzoni-type theorem for multiplicative lattices.- Paniagua, M., Facchini, A., Gran., M. and Janelidize, G: What is the spectral category?.- Finocchiaro, C. and Tartarone, F: A survey on the local invertibility of ideals in commutative rings.- Fontana, M., Houston, E., and Park, M. H: Idempotence and divisoriality in Prufer-like domains.- Frisch, S.: Simultaneous interpolation and P-adic approximation by integer-valued polynomials.- Fusacchia, G. and Salce, L: Length functions over Prufer domains.- Kainrath, F.: On some arithmetical properties of noetherian domains.- Lombardi, H.: Spectral spaces versus distributive lattices: a dictionary.- Lucas, T. G.: Valuative Marot rings.- Prihoda, P.: Classifying modules in Add of a class of modules with semilocal endomorphism rings.- Rangaswamy, K.: The multiplicative ideal theory of Leavitt path algebras of directed graphs- a survey.- Spirito, D.: When two principal star operations are the same.- Mattiello, F., Pavon, S., and Tonolo, A: Tilting modules and tilting torsion pairs -Filtrations induced by tilting modules.