Bibliographic Details
| Title: |
A BISIMPLE INVERSE MONOID OF QUADRUPLES OF NON-NEGATIVE INTEGERS. THE MÖBIUS FUNCTION. |
| Authors: |
SCHWAB, EMIL DANIEL1 eschwab@utep.edu |
| Source: |
Discussiones Mathematicae: General Algebra & Applications. 2024, Vol. 44 Issue 1, p111-126. 16p. |
| Subjects: |
Möbius function, Integers, Monoids |
| Abstract: |
The additive monoid of non-negative integers ℕ is isomorphic to the right unit submonoid of the (bisimple) bicyclic semigroup B = ℕ x ℕ. The aim of this note is to construct a similar pair of monoids (B = ℕ x ℕ, B = ℕ x ℕ x ℕ x ℕ). The monoid B gives rise to a bisimple inverse monoid B of quadruples of non-negative integers like as Warne 's 2-dimensional bicyclic semigroup. The links with the monoid of non-negative integers ℕ and with the bicyclic semigroup may turn out to be expedient also for the computation of the corresponding Möbius functions. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
