Some Results on Factorization in Integral Domains

REFERENCES

• Anderson , D. D. , Anderson , D. F. ( 1982 ). Divisibility properties of graded domains . Canad. J. Math. XXXIV ( 1 ): 196 – 215 .
   Google Scholar
• Anderson , D. D. , Anderson , D. F. ( 1982 ). Divisorial ideals and invertible ideals in a graded domain . J. Algebra 76 : 549 – 569 .
   Web of Science ®Google Scholar
• Brookfield , G. , Rush , D. ( 2005 ). When graded domains are Schreier or pre-Schreier . J. Pure and Appl. Algebra 195 : 225 – 230 .
   Web of Science ®Google Scholar
• Chapman , S. , Halter-Koch , F. , Krause , U. ( 2002 ). Inside factorial monoids and integral domains . J. Algebra 252 : 350 – 375 .
   Web of Science ®Google Scholar
• Cohn , P. M. ( 1968 ). Bezout rings and their subrings . Proc. Cambridge Philos. Soc. 64 : 251 – 264 .
   Web of Science ®Google Scholar
• Dumitrescu , T. , Khalid , W. ( 2010 ). Almost-Schreier domains . Comm. Algebra 38 : 2981 – 2991 .
   Web of Science ®Google Scholar
• Dumitrescu , T. , Khalid , W. ( 2012 ). Almost-Schreier monoids . Algebra Universalis 67 : 19 – 28 .
   Web of Science ®Google Scholar
• Etingof , P. , Malcolmson , P. , Okoh , F. ( 2010 ). Root extensions and factorization in affine domains . Canad. Math. Bull. 53 ( 2 ): 247 – 255 .
   Web of Science ®Google Scholar
• Gilmer , R. ( 1984 ). Commutative Semigroup Rings . Chicago : The University of Chicago Press .
   Google Scholar
• Grams , A. , Warner , H. ( 1975 ). Irreducible divisors in domains of finite character . Duke Math. Journal 42 : 271 – 284 .
   Web of Science ®Google Scholar
• Ireland , K. , Rosen , M. ( 1990 ). A Classical Introduction to Modern Number Theory . New York : Springer .
   Google Scholar
• Krause , U. ( 2004 ). Semigroup rings that are inside factorial and their cale representation. In: Rings, Modules, Algebras, and Abelian Groups. Lecture Notes in Pure and Appl. Math., Vol. 236. New York: Dekker, pp. 353–363 .
   Google Scholar
• Malcolmson , P. , Okoh , F. ( 2006 ). A class of integral domains between factorial domains and IDF-domains . Houston J. Math. 32 ( 2 ): 399 – 421 .
   Web of Science ®Google Scholar
• Malcolmson , P. , Okoh , F. ( 2009 ). Polynomial extensions of IDF-domains and of IDPF-domains . Proc. Amer. Math. Soc. ( 2 ): 431 – 437 .
   Web of Science ®Google Scholar
• Zafrullah , M. ( 1985 ). A general theory of almost factoriality . Manuscripta Mathematica ( 51 ): 29 – 62 .
   Google Scholar
• Zafrullah , M. ( 1987 ). On a property of pre-Schreier domains . Comm. Algebra ( 15 ): 1895 – 1920 .
   Google Scholar
• Communicated by E. Puczylowski.
   Google Scholar