Geodesic
Diversity in inside factorial monoids
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 3, pp. 811-827
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In a recent paper (Diversity in Monoids, Czech. Math. J. 62 (2012), 795–809), the last two authors introduced and developed the monoid invariant “diversity” and related properties “homogeneity” and “strong homogeneity”. We investigate these properties within the context of inside factorial monoids, in which the diversity of an element counts the number of its different almost primary components. Inside factorial monoids are characterized via diversity and strong homogeneity. A new invariant complementary to diversity, height, is introduced. These two invariants are connected with the well-known invariant of elasticity.
In a recent paper (Diversity in Monoids, Czech. Math. J. 62 (2012), 795–809), the last two authors introduced and developed the monoid invariant “diversity” and related properties “homogeneity” and “strong homogeneity”. We investigate these properties within the context of inside factorial monoids, in which the diversity of an element counts the number of its different almost primary components. Inside factorial monoids are characterized via diversity and strong homogeneity. A new invariant complementary to diversity, height, is introduced. These two invariants are connected with the well-known invariant of elasticity.
DOI : 10.1007/s10587-012-0047-0
Classification : 11B75, 11N80, 13A05, 20M05, 20M14
Keywords: factorization; monoid; elasticity; diversity 
@article{10_1007_s10587_012_0047_0,
     author = {Krause, Ulrich and Maney, Jack and Ponomarenko, Vadim},
     title = {Diversity in inside factorial monoids},
     journal = {Czechoslovak Mathematical Journal},
     pages = {811--827},
     year = {2012},
     volume = {62},
     number = {3},
     doi = {10.1007/s10587-012-0047-0},
     mrnumber = {2984636},
     zbl = {1265.20061},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0047-0/}
}
TY  - JOUR
AU  - Krause, Ulrich
AU  - Maney, Jack
AU  - Ponomarenko, Vadim
TI  - Diversity in inside factorial monoids
JO  - Czechoslovak Mathematical Journal
PY  - 2012
SP  - 811
EP  - 827
VL  - 62
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0047-0/
DO  - 10.1007/s10587-012-0047-0
LA  - en
ID  - 10_1007_s10587_012_0047_0
ER  - 
%0 Journal Article
%A Krause, Ulrich
%A Maney, Jack
%A Ponomarenko, Vadim
%T Diversity in inside factorial monoids
%J Czechoslovak Mathematical Journal
%D 2012
%P 811-827
%V 62
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0047-0/
%R 10.1007/s10587-012-0047-0
%G en
%F 10_1007_s10587_012_0047_0
Krause, Ulrich; Maney, Jack; Ponomarenko, Vadim. Diversity in inside factorial monoids. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 3, pp. 811-827. doi: 10.1007/s10587-012-0047-0

[1] Anderson, D. D., Anderson, D. F.: Elasticity of factorizations in integral domains. J. Pure Appl. Algebra 80 (1992), 217-235. | DOI | MR | Zbl

[2] Chapman, S. T., Halter-Koch, F., Krause, U.: Inside factorial monoids and integral domains. J. Algebra 252 (2002), 350-375. | DOI | MR | Zbl

[3] Chapman, S. T., Krause, U.: Cale monoids, Cale domains, and Cale varieties. Arithmetical properties of commutative rings and monoids. Boca Raton, FL: Chapman & Hall/CRC. Lecture Notes in Pure and Applied Mathematics 241 142-171 (2005). | MR | Zbl

[4] Halter-Koch, F.: Ideal Systems. An Introduction to Multiplicative Ideal Theory. Pure and Applied Mathematics, Marcel Dekker. 211. New York (1998). | MR | Zbl

[5] Krause, U.: Eindeutige Faktorisierung ohne ideale Elemente. Abh. Braunschw. Wiss. Ges. 33 (1982), 169-177 German. | MR | Zbl

[6] Krause, U.: A characterization of algebraic number fields with cyclic class group of prime power order. Math. Z. 186 (1984), 143-148. | DOI | MR | Zbl

[7] Krause, U.: Semigroups that are factorial from inside or from outside. Lattices, semigroups, and universal algebra, Proc. Int. Conf., Lisbon/Port. 1988 147-161 (1990). | MR | Zbl

[8] Maney, J., Ponomarenko, V.: Diversity in monoids. Czech. Math. J 62 (2012), 795-809. | DOI | MR

[9] Valenza, R. J.: Elasticity of factorization in number fields. J. Number Theory 36 (1990), 212-218. | DOI | MR | Zbl

Cité par Sources :