INJECTIVE TRANSFORMATIONS WITH EQUAL GAP AND DEFECT
2009 ◽
Vol 79
(2)
◽
pp. 327-336
◽
Keyword(s):
AbstractSuppose that X is an infinite set and I(X) is the symmetric inverse semigroup defined on X. If α∈I(X), we let dom α and ran α denote the domain and range of α, respectively, and we say that g(α)=|X/dom α| and d(α)=|X/ran α| is the ‘gap’ and the ‘defect’ of α, respectively. In this paper, we study algebraic properties of the semigroup $A(X)=\{\alpha \in I(X)\mid g(\alpha )=d(\alpha )\}$. For example, we describe Green’s relations and ideals in A(X), and determine all maximal subsemigroups of A(X) when X is uncountable.
2004 ◽
Vol 69
(1)
◽
pp. 87-106
◽
1999 ◽
Vol 60
(2)
◽
pp. 303-318
◽
Keyword(s):
2017 ◽
Vol 16
(12)
◽
pp. 1750223
◽
2011 ◽
Vol 2011
◽
pp. 1-14
2012 ◽
Vol 87
(3)
◽
pp. 462-479
◽
2010 ◽
Vol 82
(2)
◽
pp. 305-321
◽
Keyword(s):
2006 ◽
Vol 74
(3)
◽
pp. 393-409
◽
2007 ◽
Vol 17
(03)
◽
pp. 567-591
◽