Quasi-Going-up Rings

• Autores: Andrew J. Hetzel
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 30, Nº 2, 2004, págs. 357-392
• Idioma: inglés
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• Resumen

  • 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.