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A NOTE ON ASCEND AND DESCEND OF FACTORIZATION PROPERTIES

  • Shah Tariq (DEPARTMENT OF MATHEMATICS, QUAID-I-AZAM UNIVERSITY ISLAMABAD)
  • Published : 2006.05.01

Abstract

In this paper we extend the study of ascend and descend of factorization properties (for atomic domains, domains satisfying ACCP, bounded factorization domains, half-factorial domains, pre-Schreier and semirigid domains) to the finite factorization domains and idf-domains for domain extension $A\;{\subseteq}\;B$.

Keywords

References

  1. D. D. Anderson and D. F. Anderson, Elasticity of factorizations in integral do- mains, J. Pure Appl. Algebra 80 (1992), no. 3, 217-235 https://doi.org/10.1016/0022-4049(92)90144-5
  2. D. D. Anderson, D. F. Anderson, and M. Zafrullah, Factorization in integral domains, II, J. Algebra 152 (1992), no. 1, 78-93 https://doi.org/10.1016/0021-8693(92)90089-5
  3. D. D. Anderson, D. F. Anderson, and M. Zafrullah, Factorization in integral domains, J. Pure Appl. Algebra 69 (1990), no. 1, 1-19 https://doi.org/10.1016/0022-4049(90)90074-R
  4. D. D. Anderson and B. Mullinns, Finite Factorization Domains, Proc. Amer. Math. Soc. 124 (1996), no. 2, 389-396
  5. P. M. Cohn, Bezout rings and their subrings, Proc. Cambridge Philos. Soc. 64 (1968), 251-264
  6. R. Gilmer, Multiplicative Ideal Theory, Marcel Dekker, New York, 1972
  7. A. Grams, Atomic rings and the ascending chain condition for principal ideals, Proc. Cambridge Philos. Soc. 75 (1974), 321-329
  8. N. Radu, S. O. Ibrahim Al-Salihi, and T. Shah, Ascend and descend of factor- ization properties, Rev. Roumaine Math. Pures Appl. 45 (2000), 4, 659-669
  9. M. Roitman, Polynomial extensions of atomic domains, J. Pure Appl. Algebra 87 (1993), no. 2, 187-199 https://doi.org/10.1016/0022-4049(93)90122-A
  10. M. Zafrullah, Semirigid GCD domain, Manuscripta Math. 17 (1975), no. 1, 55- 66 https://doi.org/10.1007/BF01154282
  11. M. Zafrullah, On a property of pre-Schreier domains, Comm. Algebra 15 (1987), no. 9, 1895-1920 https://doi.org/10.1080/00927878708823512
  12. A. Zaks, Half factorial domain, Bull. Amer. Math. Soc. 82 (1976), no. 6, 721-723 https://doi.org/10.1090/S0002-9904-1976-14130-4
  13. A. Zaks, Atomic rings without a.c.c. on principal ideals, J. Algebra 74 (1982), no. 1, 223-231 https://doi.org/10.1016/0021-8693(82)90015-1