The $Q$-ideals in polynomial rings and the $Q$-modules over polynomial rings

In this paper we introduce the new categories of ideals in commutative rings of polynomials and of modules over rings of polynomials. This material proposes the definitions of linear ideal, $Q$ ideal of ring of commutative polynomials over a field, $Q$ radical, linear homomorphism between rings of polynomials and investigates the features of such objects. We cast the definition of $Q$ module over a ring of polynomials and examine the structure of such modules. In particular, it is developed the theory of primary decomposition of $Q$ modules. Also we prove that arbitrary $Q$ module can be decomposed in direct sum of torsion-free modules.