During the last 20 years, the theory involving the structure of the arithmetic and ideal theory of various algebraic structures has been a popular topic and taken several important steps forward. Many applications of this theory, with particular attention to the multiplicative monoids of integral domains and their combinatorial or numerical applications to ring theory, have appeared throughout the mathematical literature. It is the aim of this session to review recent developments in this area by bringing together researchers from different areas of algebra under the umbrella of commutative monoids, semigroups, and rings. Topics to be covered include multiplicative ideal theory and general ideal systems, arithmetic in Krull and Prüfer monoids, commutative monoid rings, integer-valued polynomials, numerical monoids and congruence monoids, direct sum decompositions of modules, and various aspects of non-unique factorization.
The abstracts of the talks can be found at the website of the meeting.
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Carmelo Cisto (University of Messina, ITALY), On factorization invariants of ideal extensions of free commutative monoids, joint work with Pedro A. García Sánchez (University of Granada, SPAIN), and David Llena (University of Almeria, SPAIN)
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Gyu Whan Chang (Incheon National University, SOUTH KOREA), Discrete valuation overrings of a Noetherian ring
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Jim Coykendall (Clemson University, USA), Norms and elasticities in rings of algebraic integers, joint work with Jared Kettinger (Clemson University, USA)
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Antonino Ficarra (University of Évora, PORTUGAL), Asymptotic behaviour of the v-number of homogeneous ideals
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Carmelo Antonio Finocchiaro (University of Catania, ITALY), Multiplicative lattices, their primes and spectral spaces
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Pedro A. García-Sánchez (University of Granada, SPAIN), The isomorphism problem for ideal class monoids of numerical semigroups
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David J. Grynkiewicz (University of Memphis, USA), On an Inverse Zero-sum Question for Rank Two Groups, joint work with John Ebert (University of Memphis, USA)
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Lorenzo Guerrieri (Jagiellonian University in Krakow, POLAND), Egyptian integral domains and the ring of reciprocals, joint work with Neil Epstein (George Mason University, USA) and K. Alan Loper (Ohio State University, USA)
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Valentin Havlovec (Graz University of Technology, AUSTRIA), Integer-valued polynomials over subrings of matrix algebras
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Alessio Moscariello (University of Catania, ITALY), Bounds for syzigies of monomial curves, joint work with Giulio Caviglia (Purdue University, USA), and Alessio Sammartano (Politecnico di Milano, ITALY)
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Giulio Peruginelli (Università di Padova, ITALY), Nontriviality of rings of integral-valued polynomials, joint work with Nicholas J. Werner (State Univ. of New York at Old Westbury, USA)
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Paul Pollack (University of Georgia, USA), Elasticity of orders in quadratic fields
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Harold Polo (University of California at Irvine, USA), Integer-Valued Polynomials for Semidomains, joint work with Scott Chapman (Sam Houston State University, USA), and Nathan Kaplan (University of California at Irvine, USA)
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Andreas Reinhart (University of Graz, AUSTRIA), On the arithmetic of the monoid of plus-minus weighted zero-sum sequences, joint work with Florin Fabsits (University of Graz, AUSTRIA), Alfred Geroldinger (University of Graz, AUSTRIA), and Qinghai Zhong (University of Graz, AUSTRIA)
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Wolfgang A. Schmid (University of Paris 8, FRANCE), Differences in sets of lengths for monoids of plus-minus weighted zerosum sequences, joint work with Kamil Merito (University of Paris 8, FRANCE) and Oscar Ordaz (Universidad Central de Venezuela, VENEZUELA)
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Francresca Tartarone (Università degli Studi Roma Tre, ITALY), Star operations related to Polynomial closure, joint work with Dario Spirito (Università degli Studi di Udine)
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Daniel Z. Vitas (University of Ljubljana, SLOVENIA), Skew Mal'cev-Neumann Series Ring Over a Dedekind Domain, joint work with Daniel Smertnig (University of Ljubljana, SLOVENIA)