IJPAM: Volume 80, No. 4 (2012)
TRANSFORMATIONS WITH RESTRICTED RANGE:
GREEN'S RELATIONS AND PARTIAL ORDERS
Department of Mathematics
Faculty of Science
Chiang Mai University
Chiangmai 50200, THAILAND
Abstract. Let be any vector space and the set of all partial injective linear transformations defined on , that is, all injective linear transformations where are subspaces of . Then is a semigroup under composition. Let be a subspace of . Define . So is a subsemigroup of . In this paper, we present the largest regular subsemigroup of and determine its Green's relations. Furthermore, we study the natural partial order on in terms of domains and images, compare with the subset order and find elements of which are compatible.
Received: August 27, 2012
AMS Subject Classification: 20M20
Key Words and Phrases: regular elements, Green's relations, injective partial linear transformation semigroups, natural order, compatibility
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395