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math.AC2013★ 4 cited
Commuting matrices, and modules over Artinian local rings
George M. Bergman
Gerstenhaber showed in 1961 that any commuting pair of n x n matrices over a field k generates a k-algebra A of k-dimension \leq n. A well-known example shows that the correspondin…
math.AC2012★ 1 cited
Thoughts on Eggert's Conjecture
George M. Bergman
Eggert's Conjecture says that if R is a finite-dimensional nilpotent commutative algebra over a perfect field F of characteristic p, and R^{(p)} is the image of the p-th power map…
math.AC2003★ 8 cited
Can one factor the classical adjoint of a generic matrix?
George M. Bergman
Let k be a field, n a positive integer, X a generic nxn matrix over k (i.e., a matrix (x_{ij}) of n^2 independent indeterminates over the polynomial ring k[x_{ij}]), and adj(X) its…