Abstract:
Linear algebra over distributive lattices, Boolean algebras and semirings etc. has a long history, as well as holds an important position in the modern theory of linear algebra due to their applications to computer science, optimizations and theoretical physics [3, 7].
In this project following the idea of Gudder and Later Molière, we have developed inner product spaces on zerosumfree semi rings. Since every Boolean algebra is a zerosumfree semiring, our results generalize the corresponding results on the Boolean inner product
