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- W17476758 abstract "In this chapter we shall develop the concepts of a ringoid and a vectoid as well as those of ordered or weakly ordered ringoids and vectoids. The development will be self-contained and, in particular, independent of Chapter 1. Chapters 3 and 4 will bring the contents of the first two chapters together. This chapter begins with the definition of a ringoid and the derivation of its most important properties. Then we show that the power set of a ringoid is a ringoid, that the matrices over an ordered or weakly ordered ringoid form an ordered or weakly ordered ringoid, and that the complexification of a weakly ordered ringoid also leads to a weakly ordered ringoid. Then we define the concept of a vectoid and derive its properties. The power set of a vectoid turns out to be a vectoid. The n-tuples over a ringoid R form a vectoid over R, as do the matrices over R. Finally, we show that ringoids and vectoids, the ordering of which is only conditionally complete, can always be completed without loss of algebraic or order properties." @default.
- W17476758 created "2016-06-24" @default.
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- W17476758 date "1981-01-01" @default.
- W17476758 modified "2023-09-27" @default.
- W17476758 title "RINGOIDS AND VECTOIDS" @default.
- W17476758 doi "https://doi.org/10.1016/b978-0-12-428650-4.50007-5" @default.
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