Abstract
We prove that every prime variety of associative algebras over an infinite field of characteristic p>0 is generated by either a unital algebra or a nilalgebra of bounded index. We show that the Engel verbally prime T-ideals remain verbally prime as we impose the identity \( x^{p^N } = 0 \) for sufficiently large N. We then describe all prime varieties in an interesting class of varieties of associative algebras.
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