FACTORIZATION IN PRÜFER DOMAINS
Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 401-409

Voir la notice de l'article provenant de la source Cambridge University Press

We construct a norm on the nonzero elements of a Prüfer domain and extend this concept to the set of ideals of a Prüfer domain. These norms are used to study factorization properties Prüfer of domains.
COYKENDALL, JIM; HASENAUER, RICHARD ERWIN. FACTORIZATION IN PRÜFER DOMAINS. Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 401-409. doi: 10.1017/S0017089517000179
@article{10_1017_S0017089517000179,
     author = {COYKENDALL, JIM and HASENAUER, RICHARD ERWIN},
     title = {FACTORIZATION {IN} {PR\"UFER} {DOMAINS}},
     journal = {Glasgow mathematical journal},
     pages = {401--409},
     year = {2018},
     volume = {60},
     number = {2},
     doi = {10.1017/S0017089517000179},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000179/}
}
TY  - JOUR
AU  - COYKENDALL, JIM
AU  - HASENAUER, RICHARD ERWIN
TI  - FACTORIZATION IN PRÜFER DOMAINS
JO  - Glasgow mathematical journal
PY  - 2018
SP  - 401
EP  - 409
VL  - 60
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000179/
DO  - 10.1017/S0017089517000179
ID  - 10_1017_S0017089517000179
ER  - 
%0 Journal Article
%A COYKENDALL, JIM
%A HASENAUER, RICHARD ERWIN
%T FACTORIZATION IN PRÜFER DOMAINS
%J Glasgow mathematical journal
%D 2018
%P 401-409
%V 60
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000179/
%R 10.1017/S0017089517000179
%F 10_1017_S0017089517000179

[1] 1. Anderson, D. F. and El Abidine, D. N., Factorization in integral domains III, J. Pure Appl. Algebra 135 (2) (1999), 107–127. MR 1667552 Google Scholar | DOI

[2] 2. Anderson, D. D., Anderson, D. F. and Zafrullah, M., Factorization in integral domains II, J. Algebra 152 (1992), 78–93. Google Scholar | DOI

[3] 3. Anderson, D. D., Anderson, D. F. and Zafrullah, M., Factorization in integral domains, J. Pure Appl. Algebra 69 (1990), 1–19. Google Scholar | DOI

[4] 4. Bazzoni, S., Groups in the class semigroup of a Prüfer domain of finite character, Comm. Algebra 28 (11) (2000), 5157–5167. MR 1785492 Google Scholar | DOI

[5] 5. Dumitrescu, T. and Zafrullah, M., Characterizing domains of finite *-character, J. Pure Appl. Algebra 214 (11) (2010), 2087–2091. MR 2645341 Google Scholar | DOI

[6] 6. Fontana, M., Houston, E. and Lucas, T., Factoring ideals in Prüfer domains, J. Pure Appl. Algebra 211 (1) (2007), 1–13. MR 2333758 Google Scholar | DOI

[7] 7. Fuchs, L., Partially ordered algebraic systems (Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963). MR 0171864 Google Scholar

[8] 8. Fuchs, L. and Mosteig, E., Ideal theory in Prüfer domains–an unconventional approach, J. Algebra 252 (2) (2002), 411–430. MR 1925145 Google Scholar | DOI

[9] 9. Gilmer, Robert, Multiplicative ideal theory, Queen's Papers in Pure and Applied Mathematics, vol. 90 (Queen's University, Kingston, ON, 1992), Corrected reprint of the 1972 edition. MR 1204267 Google Scholar

[10] 10. Gonshor, H., An introduction to the theory of surreal numbers, London Mathematical Society Lecture Note Series, vol. 110 (Cambridge University Press, Cambridge, 1986). MR 872856 Google Scholar | DOI

[11] 11. Grams, A., Atomic rings and the ascending chain condition for principal ideals, Proc. Cambridge Philos. Soc. 75 (1974), 321–329. MR 0340249 Google Scholar | DOI

[12] 12. Hasenauer, R. E., Normsets of almost Dedekind domains and atomicity, J. Commut. Algebra 8 (1) (2016), 61–75. MR 3482346 Google Scholar | DOI

[13] 13. Alan Loper, K. and Lucas, T. G., Factoring ideals in almost Dedekind domains, J. Reine Angew. Math. 565 (2003), 61–78. MR 2024646 Google Scholar

[14] 14. Ohm, J., Some counterexamples related to integral closure in D[[x]], Trans. Amer. Math. Soc. 122 (1966), 321–333. MR 0202753 Google Scholar

[15] 15. Olberding, B., Factorization into radical ideals, Arithmetical properties of commutative rings and monoids, Lect. Notes Pure Appl. Math., vol. 241 (Chapman & Hall/CRC, Boca Raton, FL, 2005), 363–377. MR 2140708 Google Scholar

Cité par Sources :