Commutative products of linear $\Omega$-algebras

In this paper we study $\mathbf P$-products of $\Omega$-algebras which are linear over some field. We characterize the subalgebras of the $\mathbf P$-products for the case when $\mathbf P$ consists of zero order commutative identities, and the subalgebra belongs to the manifold $\mathfrak M_{\mathbf P}$. We investigate the question of the structure of an arbitrary subalgebra of the $\mathbf P$-product, as well as some cases of $\mathbf P$-products for commutative identities of nonzero order. We look into the possibility of $\mathbf P$-decomposing a linear $\Omega$-algebra from an arbitrary manifold $\mathfrak M_{\mathbf S}$ and give necessary conditions for this.