Let F be an infinite field of characteristic different from two and E be the unitary Grassmann algebra of an infinite dimensional F-vector space L. Denote by E_gr an arbitrary \(\mathbb {Z}_{2}\)-grading on E such that the subspace L is homogeneous. We consider E_gr ⊗ E^⊗n as a \((\mathbb {Z}_{2}\times {\mathbb {Z}_{2}^{n}})\)-graded algebra, where the grading on E is supposed to be the canonical one, and we find its graded ideal of identities.

中文翻译：

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格拉斯曼代数的几个张量积的梯度恒等式

令F为特性不同于2的无限场，令E为无限维F向量空间L的theGrassmann代数。表示由Ë_克ř任意\（\ mathbb {Z} _ {2} \）上-grading Ë使得子空间大号是均匀的。我们认为Ë_克ř ⊗ Ë ^{⊗ Ñ}作为\（（\ mathbb {Z} _ {2} \倍{\ mathbb {Z} _ {2} ^ {N}}）\） -graded代数，分级，其中关于E的假设应该是规范的，我们发现它的恒等身份理想。