Resumen de Quasi-Going-up Rings

Andrew J. Hetzel

• We introduce and develop the theory of "quasi-going-up domains," a concept dual to going-down domains. By characterizing quasi-going-up domains as a particular type of going-down domain, we show that, in addition to Prüfer domains, the pseudo-valuation domains of Hedstrom and Houston are examples of quasi- going-up domains. We also define and develop the companion notions of "absolutely quasi-going-up domain" and "universally quasi-going-up domain." Both turn out to be examples of going-down domains and, in fact, the latter are precisely the i-domains of Papick. We conclude by defining and exploring "quasi-going-up rings," a generalization of quasi-going-up domains to the context of commutative rings with zero-divisors.