Semigroups that are Factorial from Inside or from Outside

Ulrich Krause
Additional contact information
Ulrich Krause: Universität Bremen, FB Mathematik/Informatik

A chapter in Lattices, Semigroups, and Universal Algebra, 1990, pp 147-161 from Springer

Abstract: Abstract The multiplicative semigroup of natural numbers ℕ = {1, 2,...} is factorial, i.e. every number ≠ 1 has a unique factorization into irreducible numbers (up to the ordering of the factors). Subsemigroups of ℕ however need not be factorial. Consider for example the well-known Hilbert semigroup H = 4ℤ+ + 1 = {4n + 1 ∣ n∈ℕ+} with the multiplication operation. (Thereby ℕ+ = {n∈ℕ | n ≥ 0}, ℕ = {0, ±1, ±2,...}.) The number 441, e.g, factorizes in H in the two essentially different ways 21 ·21 = 441 = 9 ·49 into numbers which are irreducible within H. (Obviously none of these irreducible numbers can be prime within H.)

Keywords: Prime Ideal; Finite Type; Principal Ideal; Commutative Semigroup; Irreducible Element (search for similar items in EconPapers)
Date: 1990
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-2608-1_17

Ordering information: This item can be ordered from
http://www.springer.com/9781489926081

DOI: 10.1007/978-1-4899-2608-1_17

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().