Diversity in inside factorial monoids

Ulrich Krause; Jack Maney; Vadim Ponomarenko

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 3, page 811-827
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Krause, Ulrich, Maney, Jack, and Ponomarenko, Vadim. "Diversity in inside factorial monoids." Czechoslovak Mathematical Journal 62.3 (2012): 811-827. <http://eudml.org/doc/246571>.

@article{Krause2012,
abstract = {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.},
author = {Krause, Ulrich, Maney, Jack, Ponomarenko, Vadim},
journal = {Czechoslovak Mathematical Journal},
keywords = {factorization; monoid; elasticity; diversity; factorizations into almost primary elements; inside factorial monoids; commutative cancellative monoids; diversity; elasticity; numbers of almost primary components},
language = {eng},
number = {3},
pages = {811-827},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Diversity in inside factorial monoids},
url = {http://eudml.org/doc/246571},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Krause, Ulrich
AU - Maney, Jack
AU - Ponomarenko, Vadim
TI - Diversity in inside factorial monoids
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 3
SP - 811
EP - 827
AB - 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.
LA - eng
KW - factorization; monoid; elasticity; diversity; factorizations into almost primary elements; inside factorial monoids; commutative cancellative monoids; diversity; elasticity; numbers of almost primary components
UR - http://eudml.org/doc/246571
ER -

References

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  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). (2005) Zbl1100.20040MR2140690
  4. Halter-Koch, F., Ideal Systems. An Introduction to Multiplicative Ideal Theory, Pure and Applied Mathematics, Marcel Dekker. 211. New York (1998). (1998) Zbl0953.13001MR1828371
  5. Krause, U., Eindeutige Faktorisierung ohne ideale Elemente, Abh. Braunschw. Wiss. Ges. 33 (1982), 169-177 German. (1982) Zbl0518.20062MR0693175
  6. Krause, U., 10.1007/BF01161801, Math. Z. 186 (1984), 143-148. (1984) Zbl0522.12006MR0741299DOI10.1007/BF01161801
  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). (1990) Zbl0736.20039MR1085077
  8. Maney, J., Ponomarenko, V., 10.1007/s10587-012-0046-1, Czech. Math. J 62 (2012), 795-809. (2012) MR2984635DOI10.1007/s10587-012-0046-1
  9. Valenza, R. J., 10.1016/0022-314X(90)90074-2, J. Number Theory 36 (1990), 212-218. (1990) Zbl0721.11043MR1072466DOI10.1016/0022-314X(90)90074-2

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