Geodesic
Characterizations of *-Multiplication Domains
Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 48-52

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DOI

Let * be a finite-type star-operation on an integral domain D. If D is integrally closed, then D is a *-multiplication domain (the *-finite *-ideals form a group) if and only if each upper to 0 in D[x] contains an element f with c(f)* = D. A finite-type star operation on D[x] naturally induces a finite-type star operation on D, and, if each *-prime ideal P of D[x] satisfies P ∩ D = 0 or P = (P ∩ D)D[x], then D[x] is a *-multiplication domain if and only if D is.
DOI : 10.4153/CMB-1984-007-2
Mots-clés : 13F05, 13F20, 13G05 
Houston, Evan G.; Malik, Saroj B.; Mott, Joe L. Characterizations of *-Multiplication Domains. Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 48-52. doi: 10.4153/CMB-1984-007-2
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     title = {Characterizations of {*-Multiplication} {Domains}},
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     year = {1984},
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     doi = {10.4153/CMB-1984-007-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-007-2/}
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