Embedding truncated skew polynomial rings into matrix rings and embedding of a ring into 2x2 supermatrices

摘要

For an endomorphism s of R with s^{t}=1 we prove that the truncatedpolynomial ring (algebra) R[w,s]/(w^{t}) embeds into M_{t}(R[z]/(z^{t})). Foran involution we exhibit an embedding of R into M_{2,1}^{s}(R), whereM_{2,1}^{s}(R) is the algebra of the so called (s,2,1) supermatrices.