query: How to distinguish vector space from $k$-algebra?
positive_passages.docid: 79460
positive_passages.text: Atiyah-Macdonald, Exercise 8.3: Artinian iff finite k-algebra.
negative_passages.docid: 26989
negative_passages.text: Show that C[0,1] is a vector space
negative_passages.docid: 156457
negative_passages.text: Show that $K[x,xy,xy^2,\dots]$ is not Noetherian
negative_passages.docid: 29756
negative_passages.text: Classsifying 1- and 2- dimensional Algebras, up to Isomorphism
negative_passages.docid: 28402
negative_passages.text: Number of bases of an n-dimensional vector space over q-element field.
negative_passages.docid: 66546
negative_passages.text: Tensor product of reduced $k$-algebras must be reduced?
negative_passages.docid: 116883
negative_passages.text: About ideals in a ring which is a $k$ vector space
negative_passages.docid: 156679
negative_passages.text: $K[X,Y]/(XY-1)$ not isomorphic to $K[T]$
negative_passages.docid: 15300
negative_passages.text: How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
negative_passages.docid: 92510
negative_passages.text: Proving a vector space is infinite-dimensional
negative_passages.docid: 89058
negative_passages.text: Question on finite Vector Spaces, injective, surjective and if $V$ is not finite
negative_passages.docid: 67191
negative_passages.text: When is the union of a family of subspaces of a vector space also a subspace?
negative_passages.docid: 141833
negative_passages.text: Is it possible to construct a quasi-vectorial space without an identity element?
negative_passages.docid: 6101
negative_passages.text: Are $\mathbb{C} \otimes _\mathbb{R} \mathbb{C}$ and $\mathbb{C} \otimes _\mathbb{C} \mathbb{C}$ isomorphic as $\mathbb{R}$-vector spaces?
negative_passages.docid: 151425
negative_passages.text: Does $\mathbb{R}^n$ have a real vector space structure with dimension other than $n$?
negative_passages.docid: 44065
negative_passages.text: If $B$ is finitely generated as a $k$-algebra, and $\phi:A\to B$ is a $k$-algebra map, is $\phi^{-1}(M)$ maximal for any maximal $M\subset B$?
negative_passages.docid: 129810
negative_passages.text: What kind of vector spaces have exactly one basis?