Author:
Fikioris George,Fikioris Giannis
Abstract
AbstractA recent paper studied an inverse submonoid $$M_{n}$$
M
n
of the rook monoid, by representing the nonzero elements of $$M_{n}$$
M
n
via certain triplets belonging to $${\mathbb {Z}}^3$$
Z
3
. In this note, we allow the triplets to belong to $${\mathbb {R}}^3$$
R
3
. We thus study a new inverse monoid $$\overline{M}_{n}$$
M
¯
n
, which is a supermonoid of $$M_{n}$$
M
n
. We point out similarities and find essential differences. We show that $$\overline{M}_{n}$$
M
¯
n
is a noncommutative, periodic, combinatorial, fundamental, completely semisimple, and strongly $${E}^{*}$$
E
∗
-unitary inverse monoid.
Funder
National Technical University of Athens
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
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