The Ideal Structure of Semigroups of Linear Transformations with Upper Bounds on Their Nullity or Defect

Suppose V is a vector space with dim V = p ≥ q ≥ ℵ 0 , and let T(V) denote the semigroup (under composition) of all linear transformations of V. For α ∈ T (V), let ker α and ran α denote the "kernel" and the "range" of α, and write n(α) = dim ker α and d(α) = codim ran α. In this...

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Bibliographic Details
Published in:Communications in algebra 2009-07, Vol.37 (7), p.2522-2539
Main Authors: Mendes-Gonçalves, Suzana, Sullivan, R. P.
Format: Article
Language:English
Subjects:
Bi-ideal
Linear transformation semigroup
Maximal regular
Maximal right simple
Primary 20M20
Quasi-ideal
Secondary 15A04
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Summary:Suppose V is a vector space with dim V = p ≥ q ≥ ℵ 0 , and let T(V) denote the semigroup (under composition) of all linear transformations of V. For α ∈ T (V), let ker α and ran α denote the "kernel" and the "range" of α, and write n(α) = dim ker α and d(α) = codim ran α. In this article, we study the semigroups AM(p, q) = {α ∈ T(V):n(α) 
ISSN:0092-7872
1532-4125
DOI:10.1080/00927870802622932