query: Cosemisimple coalgebras and uniqueness of their cosimple decompositions
positive_passages.docid: 152443
positive_passages.text: Cosemisimple Hopf algebra and Krull-Schmidt
negative_passages.docid: 116159
negative_passages.text: Derivations on semisimple Lie algebra
negative_passages.docid: 140212
negative_passages.text: Prove that there exists a unique linear map that extends the map from a basis
negative_passages.docid: 27056
negative_passages.text: $ gl(2,\mathbb C) \cong sl(2,\mathbb C) \oplus \mathbb C $
negative_passages.docid: 37953
negative_passages.text: Primary Decomposition of $\mathbb{R^n}$ under T
negative_passages.docid: 62687
negative_passages.text: Proving Cardinality of Cosets in Abstract Algebra
negative_passages.docid: 96770
negative_passages.text: Explicit isomorphism between the four dimensional orthogonal Lie algebra and the direct sum of special linear Lie algebras of dimension 3.
negative_passages.docid: 58572
negative_passages.text: Prove two commutative linear transformations on a vector space over an algebraically closed field can be simultaneously triangularized
negative_passages.docid: 102371
negative_passages.text: Proving that two vector spaces of equal dimension are isomorphic
negative_passages.docid: 131480
negative_passages.text: Proof that composition of invertible linear transformations is invertible (without determinants)
negative_passages.docid: 80302
negative_passages.text: A module $M$ whose submodules and factor modules are semisimple but not semisimple itself
negative_passages.docid: 117131
negative_passages.text: Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$
negative_passages.docid: 56211
negative_passages.text: An operator that commutes with another operator $T$ with distinct characteristic values is a polynomial in $T$
negative_passages.docid: 34712
negative_passages.text: Decomposable elements of $\Lambda^k(V)$
negative_passages.docid: 120035
negative_passages.text: Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$
negative_passages.docid: 131843
negative_passages.text: Cartan subalgebras of a semisimple Lie algebra
negative_passages.docid: 153574
negative_passages.text: Uniqueness of Artin-Wedderburn decomposition