Geodesic
ON THE ARITHMETIC OF MORI MONOIDS AND DOMAINS
Glasgow mathematical journal, Tome 62 (2020) no. 2, pp. 313-322

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

Let R be a Mori domain with complete integral closure $\widehat R$, nonzero conductor $\mathfrak f= (R: \widehat R)$, and suppose that both v-class groups ${{\cal C}_v}(R)$ and ${{\cal C}_v}(3\widehat R)$ are finite. If $R \mathfrak f$ is finite, then the elasticity of R is either rational or infinite. If $R \mathfrak f$ is artinian, then unions of sets of lengths of R are almost arithmetical progressions with the same difference and global bound. We derive our results in the setting of v-noetherian monoids. 
ZHONG, QINGHAI. ON THE ARITHMETIC OF MORI MONOIDS AND DOMAINS. Glasgow mathematical journal, Tome 62 (2020) no. 2, pp. 313-322. doi: 10.1017/S0017089519000132
@article{10_1017_S0017089519000132,
     author = {ZHONG, QINGHAI},
     title = {ON {THE} {ARITHMETIC} {OF} {MORI} {MONOIDS} {AND} {DOMAINS}},
     journal = {Glasgow mathematical journal},
     pages = {313--322},
     year = {2020},
     volume = {62},
     number = {2},
     doi = {10.1017/S0017089519000132},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000132/}
}
TY  - JOUR
AU  - ZHONG, QINGHAI
TI  - ON THE ARITHMETIC OF MORI MONOIDS AND DOMAINS
JO  - Glasgow mathematical journal
PY  - 2020
SP  - 313
EP  - 322
VL  - 62
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000132/
DO  - 10.1017/S0017089519000132
ID  - 10_1017_S0017089519000132
ER  - 
%0 Journal Article
%A ZHONG, QINGHAI
%T ON THE ARITHMETIC OF MORI MONOIDS AND DOMAINS
%J Glasgow mathematical journal
%D 2020
%P 313-322
%V 62
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000132/
%R 10.1017/S0017089519000132
%F 10_1017_S0017089519000132

[1] Anderson, D. D. and Anderson, D. F., Elasticity of factorizations in integral domains, J. Pure Appl. Algebra 80 (1992), 217–235. Google Scholar | DOI

[2] Anderson, D. F., Elasticity of factorizations in integral domains: A survey, Factorization in Integral Domains, Lect. Notes Pure Appl. Math., vol. 189 (Marcel Dekker, New York, 1997), 1–29. Google Scholar

[3] Baginski, P. and Chapman, S. T., Arithmetic Congruence Monoids: A Survey, Combinatorial and Additive Number Theory: CANT 2011 and 2012, in Proceedings in Mathematics and Statistics, vol. 101 (Springer, New York, 2014), 15–38. Google Scholar

[4] Barucci, V., Mori domains, in Non-Noetherian Commutative Ring Theory, Mathematics and Its Applications, vol. 520 (Kluwer Academic Publishers, Dordrecht, 2000), 57–73.10.1007/978-1-4757-3180-4_3 Google Scholar | DOI

[5] Chapman, S. T., Fontana, M., Geroldinger, A., and Olberding, B. (Editors), Multiplicative Ideal Theory and Factorization Theory, in Proceedings in Mathematics and Statistics, vol. 170 (Springer, Cham, 2016). Google Scholar

[6] Cziszter, K., Domokos, M. and Geroldinger, A., The interplay of invariant theory with multiplicative ideal theory and with arithmetic combinatorics, in Multiplicative Ideal Theory and Factorization Theory (Springer, Cham, 2016), 43–95. Google Scholar | DOI

[7] Fan, Y., Geroldinger, A., Kainrath, F. and Tringali, S., Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules, J. Algebra Appl. 11 (2017), 1750234 (42 pages). Google Scholar | DOI

[8] Fontana, M., Frisch, S., Glaz, S., Tartarone, F., and Zanardo, P. (Editor), Rings, polynomials, and modules (Springer, Cham, 2017). Google Scholar | DOI

[9] Gao, W. and Geroldinger, A., On products of k atoms, Monatsh. Math. 156 (2009), 141–157. Google Scholar

[10] Geroldinger, A., Sets of lengths, Am. Math. Monthly 123 (2016), 960–988. Google Scholar | DOI

[11] Geroldinger, A. and Halter-Koch, F., Congruence monoids, Acta Arith.112 (2004), 263–296. Google Scholar | DOI

[12] Geroldinger, A. and Halter-Koch, F., Non-Unique Factorizations. Algebraic, Combinatorial and Analytic Theory, in Pure and Applied Mathematics, vol. 278 (Chapman & Hall/CRC, Boca Raton, 2006). Google Scholar

[13] Geroldinger, A. and Hassler, W., Arithmetic of Mori domains and monoids, J. Algebra 319 (2008), 3419–3463. Google Scholar | DOI

[14] Geroldinger, A. and Hassler, W., Local tameness of v-noetherian monoids, J. Pure Appl. Algebra 212 (2008), 1509–1524. Google Scholar | DOI

[15] Geroldinger, A. and Zhong, Q., Long sets of lengths with maximal elasticity, Can. J. Math.70 (2018), 1284–1318. Google Scholar | DOI

[16] Geroldinger, A., Ramacher, S. and Reinhart, A., On v-Marot Mori rings and C-rings, J. Korean Math. Soc. 52 (2015), 1–21. Google Scholar | DOI

[17] Gotti, F., On the system of sets of lengths and the elasticity of submonoids of , . Google Scholar | arXiv

[18] Halter-Koch, F., Ideal Systems. An Introduction to Multiplicative Ideal Theory (Marcel Dekker, 1998). Google Scholar

[19] Kainrath, F., Elasticity of finitely generated domains, Houston J. Math.31 (2005), 43–64. Google Scholar

[20] Kainrath, F., Arithmetic of Mori domains and monoids: The global case, Multiplicative Ideal Theory and Factorization Theory, in Springer Proc. Math. Stat., vol. 170 (Springer, Cham, 2016), 183–218. Google Scholar

[21] Reinhart, A., On integral domains that are C-monoids, Houston J. Math. 39 (2013), 1095–1116. Google Scholar

[22] Schmid, W. A., Some recent results and open problems on sets of lengths of Krull monoids with finite class group, Multiplicative Ideal Theory and Factorization Theory, in Springer Proc. Math. Stat., vol. 170 (Springer, Cham, 2016), 323–352. Google Scholar

[23] Tringali, S., Structural properties of subadditive families with applications to factorization theory, Israel J. Math. (to appear), . Google Scholar | arXiv

[24] Zhong, Q., On elasticities of locally finitely generated monoids, . Google Scholar | arXiv

Cité par Sources :