| Title:
|
Diversity in inside factorial monoids (English) |
| Author:
|
Krause, Ulrich |
| Author:
|
Maney, Jack |
| Author:
|
Ponomarenko, Vadim |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
811-827 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
factorization |
| Keyword:
|
monoid |
| Keyword:
|
elasticity |
| Keyword:
|
diversity |
| MSC:
|
11B75 |
| MSC:
|
11N80 |
| MSC:
|
13A05 |
| MSC:
|
20M05 |
| MSC:
|
20M14 |
| idZBL:
|
Zbl 1265.20061 |
| idMR:
|
MR2984636 |
| DOI:
|
10.1007/s10587-012-0047-0 |
| . |
| Date available:
|
2012-11-10T21:19:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143027 |
| . |
| Reference:
|
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| Reference:
|
[2] Chapman, S. T., Halter-Koch, F., Krause, U.: Inside factorial monoids and integral domains.J. Algebra 252 (2002), 350-375. Zbl 1087.13510, MR 1925142, 10.1016/S0021-8693(02)00031-5 |
| Reference:
|
[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). Zbl 1100.20040, MR 2140690 |
| Reference:
|
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| Reference:
|
[5] Krause, U.: Eindeutige Faktorisierung ohne ideale Elemente.Abh. Braunschw. Wiss. Ges. 33 (1982), 169-177 German. Zbl 0518.20062, MR 0693175 |
| Reference:
|
[6] Krause, U.: A characterization of algebraic number fields with cyclic class group of prime power order.Math. Z. 186 (1984), 143-148. Zbl 0522.12006, MR 0741299, 10.1007/BF01161801 |
| Reference:
|
[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). Zbl 0736.20039, MR 1085077 |
| Reference:
|
[8] Maney, J., Ponomarenko, V.: Diversity in monoids.Czech. Math. J 62 (2012), 795-809. MR 2984635, 10.1007/s10587-012-0046-1 |
| Reference:
|
[9] Valenza, R. J.: Elasticity of factorization in number fields.J. Number Theory 36 (1990), 212-218. Zbl 0721.11043, MR 1072466, 10.1016/0022-314X(90)90074-2 |
| . |
