Integral Domains Having Nonzero Elements with Infinitely Many Prime Divisors

REFERENCES

• Anderson , D. D. , Anderson , D. F. , Zafrullah , M. ( 1990 ). Factorization in integral domains . J. Pure and Appl. Algebra 69 : 1 – 19 .
   Web of Science ®Google Scholar
• Anderson , D. D. , Anderson , D. F. , Zafrullah , M. ( 1991a ). Rings between D[X] and K[X] . Houston J. Math. 17 : 109 – 128 .
   Web of Science ®Google Scholar
• Anderson , D. F. , Houston , E. G. , Zafrullah , M. (1991b). Pseudo-integrality. Canad. Math. Bull. 34:15–22.
   Web of Science ®Google Scholar
• Cahen , P.-J . ( 1998 ). Couples d'anneaux partageant un ideal . Arch. Math. 51 : 505 – 514 .
   Google Scholar
• Costa , D. , Mott , J. L. , Zafrullah , M. ( 1978 ). The construction D + XD S [X] . J. Algebra 53 : 423 – 439 .
   Web of Science ®Google Scholar
• Coykendall , J. ( 2002 ). GD(1) and GD(2) are not preserved in integral closures . Commutative Rings . ( Compilation of the first four issues of the International Journal of Commutative Rings ). New York : Nova Science Publishers .
   Google Scholar
• Dobbs , D. , Houston , E. , Lucas , T. , Zafrullah , M. ( 1989 ). t-linked overrings and Prüfer v-multiplication domain . Comm. Algebra 17 : 2835 – 2852 .
   Web of Science ®Google Scholar
• Dobbs , D. , Houston , E. , Lucas , T. , Roitman , M. , Zafrullah , M. ( 1992 ). On t-linked overrings . Comm. Algebra 20 : 1463 – 1488 .
   Web of Science ®Google Scholar
• Dumitrescu , T. , Zafrullah , M. ( 2001 ). LCM-splitting sets in some ring extensions . Proc. Amer. Math. Soc. 130 : 1639 – 1644 .
   Google Scholar
• Gilmer , R. ( 1972 ). Multiplicative Ideal Theory . New York : Dekker .
   Google Scholar
• Grams , A. , Warner , H. ( 1975 ). Irreducible divisors in domains of finite character . Duke Math. J. 42 : 271 – 284 .
   Web of Science ®Google Scholar
• Hochster , M. ( 1973 ). Non-openness of loci in Noetherian rings . Duke Math. J. 40 : 215 – 219 .
   Web of Science ®Google Scholar
• Kang , B. G. , Park , M. H. ( 1999 ). A localization of a power series ring over a valuation domain . J. Pure Appl. Algebra 140 : 107 – 124 .
   Web of Science ®Google Scholar
• Malcolmson , P. , Okoh , F. ( 2005 ). Expansions of prime ideals . Rocky Mountain J. Math. 35 : 1689 – 1706 .
   Web of Science ®Google Scholar
• Communicated by J. Kuzmanovich.
   Google Scholar