Some results on t–locally Strong Mori domains and their rings of integer–valued polynomials

Abstract

An integral domain D is said to be t–locally Strong Mori (for short, t–LSM) if $$D_\mathfrak {m}$$ is Strong Mori for all t–maximal ideals $$\mathfrak {m}$$ of D. This paper studies some ring–theoretic properties of t–LSM domains and the algebra structure of rings of integer–valued polynomials arising from t–LSM domains. Among other things, we investigate the property of being a t–LSM domain in the t–flat overring extension, the t–Nagata ring, the polynomial ring, pullback construction and the power series ring. Also, we study $${\mathrm {Int}}(D)$$ over a t–LSM domain D. Precisely, we are interested in the Krull dimension, the trivial case and some module structure properties.