This chapter will develop from scratch the elementary theory of (quadratic) Jordan algebras over commutative rings. After a brief account of linear Jordan algebras and their most rudimentary properties over rings in which 2 is invertible, we proceed to para-quadratic algebras, which play the same role in the quadratic setting as is played by ordinary nonassociative algebras in the linear setting. Quadratic Jordan algebras are introduced. We derive a wide range of useful identities and acquaint the reader with the standard examples of special Jordan algebras, namely the Jordan algebra constructed from a unital associative algebra, from an associative algebra with involution, or from a pointed quadratic module. After a brief interlude concerning a peculiar class of two-variable identities, we investigate what are arguably the most important concepts of the theory: invertibility, isotopy, and the structure group. The chapter concludes with a concise description of the Peirce decomposition relative to an idempotent, and also relative to a complete orthogonal system of idempotents.

This Introduction lays the theoretical and methodological foundation for this work through seven theses, each of which explores how Pentecostals shape the Nigerian social context through continuous actions of their faith, the instability of the social order and the systems of meaning they seek to inscribe, the social implications of their will to power, and the various understanding of power. Through an engagement with performance studies scholars and Pentecostal studies, this chapter establishes the historical and social contexts that have driven the Pentecostal desire for power.

This Introduction lays the theoretical and methodological foundation for this work through seven theses, each of which explores how Pentecostals shape the Nigerian social context through continuous actions of their faith, the instability of the social order and the systems of meaning they seek to inscribe, the social implications of their will to power, and the various understanding of power. Through an engagement with performance studies scholars and Pentecostal studies, this chapter establishes the historical and social contexts that have driven the Pentecostal desire for power.