For questions related to syzygies. It is defined in terms of a polynomial ring of $n$ variables over a field $k$.
Let $M$ be a left $A$-module, and let $(m_i)_{i∈I}$ be a family of elements of $M$; a relationship, or syzygy, between the $m_i$ is a set $(a_i)_{i∈I}$ of elements of the ring $A$ such that $∑_{i∈I}a_im_i=0$. Thus there arises the module of syzygies, the chain complex of syzygies, etc.