query: Find composition series of Αrtinian ring, that is finite dimensional vector space
positive_passages.docid: 150911
positive_passages.text: Prove that the ring is Artinian and find a composition series of ideals
negative_passages.docid: 74128
negative_passages.text: Second exterior power of a complex vector space
negative_passages.docid: 145351
negative_passages.text: Ring of formal power series over a principal ideal domain is a unique factorisation domain
negative_passages.docid: 157585
negative_passages.text: Structure theorem of finite rings
negative_passages.docid: 86362
negative_passages.text: Cyclic vectors in a real vector space
negative_passages.docid: 145390
negative_passages.text: Formal power series ring, norm.
negative_passages.docid: 39487
negative_passages.text: Zariski Tangent Space and $k[\varepsilon]/\varepsilon^2$
negative_passages.docid: 125073
negative_passages.text: Finite-dimensional subspaces of normed vector spaces are direct summands
negative_passages.docid: 63568
negative_passages.text: Ring with finitely many zerodivisors
negative_passages.docid: 55828
negative_passages.text: What are the generators for $SL_n(\mathbb{R})$ (Michael Artin's Algebra book)
negative_passages.docid: 17748
negative_passages.text: Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?
negative_passages.docid: 34712
negative_passages.text: Decomposable elements of $\Lambda^k(V)$
negative_passages.docid: 18913
negative_passages.text: How to find a basis for the intersection of two vector spaces in $\mathbb{R}^n$?
negative_passages.docid: 143517
negative_passages.text: Isomorphisms Between a Finite-Dimensional Vector Space and its Dual
negative_passages.docid: 16602
negative_passages.text: Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
negative_passages.docid: 68526
negative_passages.text: Polynomials as vector spaces?
negative_passages.docid: 57269
negative_passages.text: A special bijection between $\mathbb{R}\times \mathbb{R}$ and $\mathbb{R}$