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Examples of Half-Factorial Domains

Published online by Cambridge University Press:  20 November 2018

Hwankoo Kim*
Affiliation:
Department of Mathematics, The University of Tennessee at Knoxville, Knoxville, TN 37996-1300, USA, email: hwankoo@utkux.utcc.utk.edu
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Abstract

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In this paper, we determine some sufficient conditions for an $A\,+\,XB\left[ X \right]$ domain to be an $\text{HFD}$. As a consequencewe give new examples of $\text{HFDs}$ of the type $A\,+\,XB\left[ X \right]$.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2000

References

[1] Anderson, D. D. and Anderson, D. F., Elasticity of factorizations in integral domains. J. Pure Appl. Algebra 80 (1992), 217235.Google Scholar
[2] Anderson, D. D. and Anderson, D. F., Elasticity of factorizations in integral domains, II. Houston J. Math. (1) 20 (1994), 115.Google Scholar
[3] Anderson, D. D., Anderson, D. F., Chapman, S. T. and Smith, W. W., Rational elasticity of factorizations in Krull domains. Proc. Amer. Math. Soc. (1) 117 (1993), 3743.Google Scholar
[4] Anderson, D. D., Anderson, D. F. and Zafrullah, M., Factorization in integral domains. J. Pure Appl. Algebra 69 (1990), 119.Google Scholar
[5] Anderson, D. D., Anderson, D. F. and Zafrullah, M., Rings between D[X] and K[X]. Houston Math. J. 17 (1991), 109129.Google Scholar
[6] Anderson, D. D., Anderson, D. F. and Zafrullah, M., Splitting the t-class group. J. Pure Appl. Algebra 74 (1991), 1737.Google Scholar
[7] Anderson, D. D., Anderson, D. F. and Zafrullah, M., Factorization in integral domains, II. J. Algebra 152 (1992), 7893.Google Scholar
[8] Anderson, D. F., Elasticity of factorizations in integral domains, a survey. Lecture Notes in Pure and Appl. Math. 189, Dekker, New York, 1997, 1–29.Google Scholar
[9] Anderson, D. F., Chapman, S. T. and Smith, W. W., Some factorization properties of Krull domains with infinite cyclic divisor class group. J. Pure Appl. Algebra 96 (1994), 97112.Google Scholar
[10] Anderson, D. F. and El Abidine, D. Nour, Factorization in integral domains, III. J. Pure Appl. Algebra, to appear.Google Scholar
[11] Anderson, D. F., Park, J., Kim, G. and Oh, H., Splitting multiplicative sets and elasticity. Comm. Algebra 26 (1998), 12571276.Google Scholar
[12] Barucci, V., Izelgue, L. and Kabbaj, S., Some factorization properties of A + XB[X] domains. Lecture Notes in Pure and Appl. Math. 185, Dekker, New York, 1997, 69–78.Google Scholar
[13] Cohn, P. M., Bézout rings and their subrings. Math. Proc. Cambridge Philos. Soc. 64 (1968), 251264.Google Scholar
[14] Coykendall, J., A characterization of polynomial rings with the half-factorial property. Lecture Notes in Pure and Appl. Math. 189, Dekker, New York, 1997, 291–294.Google Scholar
[15] Gilmer, R., Multiplicative Ideal Theory. Dekker, New York, 1972.Google Scholar
[16] Gonzalez, N., Elasticity of A + XB[X] domains. J. Pure Appl. Algebra, to appear.Google Scholar
[17] Grams, A., Atomic domains and the ascending chain condition for principal ideals. Math. Proc. Cambridge Philos. Soc. 75 (1974), 321329.Google Scholar
[18] Matsumura, H., Commutative ring theory. Cambridge Stud. Adv. Math. 8, 1990.Google Scholar
[19] Steffan, J. L., Longueurs des décompositions en produits d’éléments irréductibles dans un anneau de Dedekind. J. Algebra 102 (1986), 229236.Google Scholar
[20] Valenza, R. J., Elasticity of factorizations in number fields. J. Number Theory 36 (1990), 212218.Google Scholar
[21] Zaks, A., Half-factorial domains. Bull. Amer.Math. Soc. 82 (1976), 721724.Google Scholar
[22] Zaks, A., Half-factorial domains. Israel J. Math. 37 (1980), 281302.Google Scholar