I have a quite tough problem to solve and need an algebra that allows to "vectors" following operations:  multiplication between two vectors are componentwise that means v=(v1, v2, v3,...) multiplied by w=(w1, w2, w3,...) gives v.w = (v1 w1, v2 w2, v3 w3,...)  no scalar multiplication of vectors allowed  all mathematical operators suc as log, sin, cos, sign, etc are applied componentwise  the vectors contain only integers In general every operation seems to work here component wise. Indeed I do not even like to call them even a vector. Formally, I need to fix what type of ring/module/... and properties define exactly this algebra and what terminology I can use. It is crazy that I have solved the problem but can not expressit in a formal language, because of lacking as from natural sciences the mathematical formalism from abstract algebra. Is there anybody who can help me please. Many thanks Sam
