TY - JOUR
DO - 10.4134/BKMS.B160929
UR - https://doi.org/10.4134/BKMS.B160929
TI - UPPERS TO ZERO IN POLYNOMIAL RINGS OVER GRADED DOMAINS AND UMt-DOMAINS
T2 - 대한수학회보
AB - Let $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}\;R_{\alpha}$ be a graded integral domain, H be the set of nonzero homogeneous elements of R, and ${\star}$ be a semistar operation on R. The purpose of this paper is to study the properties of $quasi-Pr{\ddot{u}}fer$ and UMt-domains of graded integral domains. For this reason we study the graded analogue of ${\star}-quasi-Pr{\ddot{u}}fer$ domains called $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. We study several ring-theoretic properties of $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. As an application we give new characterizations of UMt-domains. In particular it is shown that R is a $gr-t-quasi-Pr{\ddot{u}}fer$ domain if and only if R is a UMt-domain if and only if RP is a $quasi-Pr{\ddot{u}}fer$ domain for each homogeneous maximal t-ideal P of R. We also show that R is a UMt-domain if and only if H is a t-splitting set in R[X] if and only if each prime t-ideal Q in R[X] such that $Q{\cap}H ={\emptyset}$ is a maximal t-ideal.
AU - Hamdi Haleh
AU - Sahandi Parviz
VL - 55
IS - 1
SP - 187
EP - 204
PY - 2018/01/31
PB - 대한수학회
SN - 1015-8634/2234-3016
LA - EN
ER -