Construction of Finite Sequences over Ring and Left-, Right-, and Bi-Modules over a Ring
نویسندگان
چکیده
This text includes definitions of finite sequences over rings and left-, right-, and bi-module over a ring, treated as functions defined for all natural numbers, but almost everywhere equal to zero. Some elementary theorems are proved, in particular for each category of sequences the schema of existence is proved. In all four cases, i.e for rings, left-, right-, and bi-modules are almost exactly the same, hovewer we do not know how to do the job in Mizar in a different way. The paper is mostly based on [2]. In particular the notion of initial segment of natural numbers is introduced which differs from that of [2] by starting with zero. This proved to be more convenient for algebraic purposes.
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