ON A SUBCLASS OF SEMISTAR GOING-DOWN DOMAINS

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International Electronic Journal of Algebra
Volume:14 Issue:14
ON A SUBCLASS OF SEMISTAR GOING-DOWN DOMAINS

ON A SUBCLASS OF SEMISTAR GOING-DOWN DOMAINS

Authors : Parviz SAHANDİ, Nematollah SHİRMOHAMMADİ

Pages : 53-68

View : 29 | Download : 9

Publication Date : 2013-12-01

Article Type : Research Paper

Abstract :Let D be an integral domain and let ? be a semistar operation on D. In this paper, we define the class of ?-quasi-going-up domains, a notion dual to the class of ?-going-down domains. It is shown that the class of ?-quasi-going-up domains is a proper subclass of ?-going-down domains and that every Prüfer-?-multiplication domain is a ?-quasi-going-up domain. Next, we prove that the ?-Nagata ring Nainsert ignore into journalissuearticles values(D, ?);, is a quasi-going-up domain if and only if D is a e?-quasi-going-up and a e?-quasi-Prüfer domain. Several new characterizations are given for ?-going-down domains. We also define the universally ?-going-down domains, and then, give new characterizations of Prüfer-?-multiplication domains.
Keywords : Semistar operation, integral domain, B´ezout domain, going down domain, going up, lying over, quasi going up, quasi going up domain

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