We study prime monomial homomorphic images of the semigroup algebra of the subsemigroup of the 2-generated free 3-nilpotent group generated by the (positive) group generators. In particular, we show that they are either PI of linear growth or primitive just-infinite of quadratic growth. This partially answers a question of Okniński.

中文翻译：

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自由零幂子群的亚半群的代数的本初多项式理想

我们研究由（正）组生成器生成的2个生成的自由3次幂群的亚半群的半群代数的半单代数的素单项同态图像。特别地，我们表明它们是线性增长的PI或二次增长的原始正无限。这部分回答了Okniński的问题。