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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 ≥ ℵ0, 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 …