Analogue for simple modules in vector space setting
A non-zero module is simple/irreducible if it has no non-trivial proper submodules. Suppose $M$ is a simple module over the ring $R$. If $R$ is a field, is there a special name for $M$? ie simple /irreducible vector space? Is there anything special about such a vector space?
There is no special name other than simply "1-dimensional $R$-vector space".