On permanental identities over matrix rings

Some ring theory from Jenő Szigeti

“…The lower bounds assumed depend on both d and n (see [7]). A variation on these assumptions on the graph which ensure the validity of the identity Q .X / D 0 on M n .˝/ can be found in [2]. It is worth to note that the proof of the matrix identity P .X / D 0 is based on the use of Swan's theorem on the signs of directed Eulerian paths, while the proof of Q .X / D 0 is based on a formula (due to Aardenne-Ehrenfest and de Bruijn) counting the number of directed Eulerian paths.…”

“…C .´k1 1 / J OE´ C .´k2 1 / J OE´ C .´k m 1 / of M m .ROE´/, still containing I.X / as an ideal. Now let ' 2 End R .M / be an arbitrary R-endomorphism of a finitely generated semisimple left R-module R M .…”

On Permanental Identities of Symmetric and Skew-Symmetric Matrices in Characteristic p

“…In [2] it was proved that C r (x 1 Ò Òx r Òy 1 Ò Òy r ) is a polynomial identity for M n (F) if and only if r ½ np where char F = p Ù 0.…”