I want to understand better when from here they say
When the requirement that the set of scalars form a field is relaxed so that it need only form a ring [..] In this case the "scalars" may be complicated objects [..]
I was studying the restriction of scalars but I really don't understand direct connection between scalars & modules.
a set of scalars can be generated directly from modules if set of scalars form a field but only if field is 'relaxed' to form a ring ?
what does this 'field relaxed' term mean in context of scalar-module relation ?
When $V$ is a vector space over a field $K$, the elements of $K$ are usually called scalars, since they can be used to scale a vector $v$ as $\lambda\cdot v$ for $\lambda\in K$. Now take the definition of a vector space and just replace the field $K$ by a ring $R$ (this is what is meant by relaxing the definition). You still want a "scalar multiplication" $R\times V\to V$ so $\lambda\cdot v$ makes sense for $\lambda\in R$ and $v\in V$. Hence your scalars are now elements of $R$. What you get is no longer a vector space but an $R$-module.