Since rings are more general than fields, modules are more general than vector spaces. The tensor product of two modules over a commutative ring is defined by taking the Cartesian product and moding out by the necessary relations to make things bilinear. (This description is very hand-wavy. A...
Rings are always postulated to be associative. Algebras need not be. An algebra is the structure obtained when an internal binary multiplication is well-defined on the vector space E (the product of two vectors is a vector) which is bilinear and distributive over addition. That's to say: ...
With VERY low expectations, I decided to make a few. Due to my research and background in chemistry, I understood the potential for how they could work. I was amazed shortly after making them. That night, I slept by the rings and I slept like a baby! Not only that, I felt a great...
Let t be an indeterminate and Rδ respective Rδ,t the Grothendieck rings of Rep(GLδ) over k respective of Rep(GLt )) over the fraction field k((t − δ)). We follow the notation 434 T. Heidersdorf, R. Weissauer of [7] and denote by (λ) or simply λ the element R(λ)...
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This study is remounted to the K-theory on the sheaves cohomologies constructed through pre-sheaves defined by the tensor product on commutative rings. The intention of this study is to establish a method- ology through commutative rings and their construction of a total tensor product ⊗ L,...
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Furthermore, magnet 210 may be modular, such as a set of superconducting rings that each have a peak magnetic-field strength of 0.5 T and that can be added, removed or moved to create different magnetic-field magnitudes and configurations. Magnet 210 may produce magnetic fields that can be ...
Furthermore, magnet 210 may be modular, such as a set of superconducting rings that each have a peak magnetic-field strength of 0.5 T and that can be added, removed or moved to create different magnetic-field magnitudes and configurations. Magnet 210 may produce magnetic fields that can be ...