论文标题
$ \ MATHBB {Z} _2 \ times \ Mathbb {z} _2 $ - $ e \ otimes e $在有限字段上的注释
A note on the $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded identities of $E \otimes E$ over a finite field
论文作者
论文摘要
令$ f $为$ char f = p $和size $ | f |的有限字段= Q $。令$ e $为统一的无限尺寸格拉斯曼代数。在此简短说明中，我们描述了$ \ mathbb {z} _2 \ times \ times \ mathbb {z} _2 $ - graded的身份$ e_ {k^{*}} \ otimes e $，其中$ e_ e_ {k^{*}} $是特定的grassmann algebra with the grassmann algebra with a grassmann algebra。 $ \ mathbb {z} _ {2} $ - 分级。最后，我们讨论了$ \ mathbb {z} _2 \ times \ times \ mathbb {z} _2 $ - graded gk-dimension $ e_ {k^*} \ otimes e $ in $ m $变量。
Let $F$ be a finite field of $char F = p$ and size $|F| = q$. Let $E$ be the unitary infinity dimensional Grassmann algebra. In this short note, we describe the $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded identities of $E_{k^{*}}\otimes E$, where $E_{k^{*}}$ is the Grassmann algebra with a specific $\mathbb{Z}_{2}$-grading. In the end, we discuss about the $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded GK-dimension of $E_{k^*}\otimes E$ in $m$ variables.
