This book is the first to be devoted entirely to fuzzy abstract algebra. It presents an up-to-date version of fuzzy commutative algebra, and focuses on the connection between L-subgroups of a group, and L-subfields of a field. In particular, an up-to-date treatment of nonlinear systems of fuzzy intersection equations is given.Contents: L-Subsets and L-SubgroupsL-Subgroups of Abelian GroupsL-Subrings and L-IdealsL-SubmodulesL-SubfieldsStructure of L-Subrings and L-IdealsAlgebraic L-Varieties and Intersection EquationsL-SubspacesGalois Theory and Group L-SubalgebrasReadership: Pure mathematicians.Key Features:Primary emphasis on the derivation of approximate equations. Less effort is devoted to their solutions and the implied physical significanceLimits the mathematics to the level commonly taught to graduate students of engineering and physical sciencesDetails are explained from ground zeroUseful to a audience engaging in both theoretical and applied research of multiphase mechanics