Ntumba, Patrice P.2022-02-042022-02-0420222021*A2022http://hdl.handle.net/2263/83629Thesis (PhD (Mathematical Sciences))--University of Pretoria, 2021.The study of Azumaya algebras over schemes has had a comparatively formidable reputation in algebraic geometry over the past decades. In this thesis, we provide in the sheaf-theoretic setting counterparts of results pertaining to involutions of the first kind on algebras of endomorphisms of faithfully projective -modules, where is a commutative ring. More precisely, let be a locally finitely presented module over an affine scheme X, and let be an involution of the first kind on . Then, there exists an invertible module over the ringed space such that . Moreover, given a vector sheaf of finite rank on a locally ringed space and involution of the first kind on and an invertible -module such that , then σ locally will depend on an invertible section of .en© 2022 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.UCTDAzumaya algebrasInvolutionsLocalizationsCoherent sheavesThesis