Editing General linear group (section)

=== Full linear monoid ===
The Full Linear Monoid, derived upon removal of the determinant's non-zero restriction, forms an algebraic structure akin to a monoid, often referred to as the full linear monoid or occasionally as the full linear semigroup or general linear monoid. Notably, it constitutes a regular semigroup.{{expand section|basic properties|date=April 2015}}
If one removes the restriction of the determinant being non-zero, the resulting algebraic structure is a [[monoid]], usually called the '''full linear monoid''',<ref name="Okniński1998">{{cite book|author=Jan Okniński|title=Semigroups of Matrices|year=1998|publisher=World Scientific|isbn=978-981-02-3445-4|at=Chapter 2: Full linear monoid}}</ref><ref name="Meakin">{{cite book|editor=C. M. Campbell|title=Groups St Andrews 2005|year=2007|publisher=Cambridge University Press|isbn=978-0-521-69470-4|page=471|chapter=Groups and Semigroups: Connections and contrast|author=Meakin}}</ref><ref name="RhodesSteinberg2009">{{cite book|author1=John Rhodes|author2=Benjamin Steinberg|title=The q-theory of Finite Semigroups|year=2009|publisher=Springer Science & Business Media|isbn=978-0-387-09781-7|page=306}}</ref> but occasionally also ''full linear semigroup'',<ref name="JespersOkniski2007">{{cite book|author1=Eric Jespers|author2=Jan Okniski|title=Noetherian Semigroup Algebras|year=2007|publisher=Springer Science & Business Media|isbn=978-1-4020-5810-3|at=2.3: Full linear semigroup}}</ref> ''general linear monoid''<ref name="Geck2013">{{cite book|author=Meinolf Geck|title=An Introduction to Algebraic Geometry and Algebraic Groups|year=2013|publisher=Oxford University Press|isbn=978-0-19-967616-3|page=132}}</ref><ref name="CanLi2014">{{cite book|author1=Mahir Bilen Can|author2=Zhenheng Li|author3=Benjamin Steinberg|author4=Qiang Wang|title=Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics|year=2014|publisher=Springer|isbn=978-1-4939-0938-4|page=142}}</ref> etc. It is actually a [[regular semigroup]].<ref name="Meakin"/>