Algebras which are nearly finite dimensional and their identities (Q1611542)

An infinite dimensional \(k\)-algebra \(R\) is called just infinite dimensional provided that every nonzero two-sided ideal has finite codimension in \(R\). The authors prove over an uncountable field \(k\) the following. If \(R\) is an affine, semiprimitive, just infinite dimensional \(k\)-algebra then either \(R\) is primitive or \(R\) satisfies a polynomial identity.