Topology transparent scheduling (TTS) has been widely studied over the last two decades, which provides guaranteed throughput for each node in the network with only knowledge of global parameters. Leveraging different mathematical approaches, the existing TTSs briefly fall into three board categories: 1) the Galois field (GF)-based; 2) the combinatory-based; and 3) the number theory-based schemes. In this letter, a new scheme via the polynomial ring is proposed as a generalization of Chinese remainder theorem (CRT)-based TTS presented recently. It brings significant improvement over the theoretic bounds of both maximum nodal degree supported and frame length required. In addition, we prove that the proposed scheme is also a generic framework of both GF and CRT-based TTS.