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Abstract: By means of a mixture of linear and nonlinear techniques, the paper treats quasi-Banach function spaces as -modules and studies the basic algebraical constructions and their interactions, placing the emphasis on tensor products. Sample result: if is an exact sequence of -modules and homomorphisms, where Y and Z are function spaces, and V is another function space, then the tensorized sequence is exact too. [Copyright &y& Elsevier]

Abstract: It is shown that every centralizer from any “metric function space” to is continuous at the origin of . As a consequence, every short exact sequence of -modules splits if is a “minimal” function space, and in particular if . There are pairs of Orlicz function spaces such that , but . [Copyright &y& Elsevier]