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- Matrix_ring abstract "In abstract algebra, a matrix ring is any collection of matrices over some ring R that form a ring under matrix addition and matrix multiplication (Lam 1999). The set of n × n matrices with entries from R is a matrix ring denoted Mn(R), as well as some subsets of infinite matrices which form infinite matrix rings. Any subring of a matrix ring is a matrix ring.When R is a commutative ring, the matrix ring Mn(R) is an associative algebra, and may be called a matrix algebra. For this case, if M is a matrix and r is in R, then the matrix Mr is the matrix M with each of its entries multiplied by r.This article assumes that R is an associative ring with a unit 1 ≠ 0, although matrix rings can be formed over rings without unity.".
- Matrix_ring wikiPageID "487541".
- Matrix_ring wikiPageLength "10590".
- Matrix_ring wikiPageOutDegree "82".
- Matrix_ring wikiPageRevisionID "689043570".
- Matrix_ring wikiPageWikiLink *-algebra.
- Matrix_ring wikiPageWikiLink 2_×_2_real_matrices.
- Matrix_ring wikiPageWikiLink Absolute_convergence.
- Matrix_ring wikiPageWikiLink Abstract_algebra.
- Matrix_ring wikiPageWikiLink Algebra_homomorphism.
- Matrix_ring wikiPageWikiLink Algebra_over_a_field.
- Matrix_ring wikiPageWikiLink Angular_momentum.
- Matrix_ring wikiPageWikiLink Artinian_ring.
- Matrix_ring wikiPageWikiLink Artin–Wedderburn_theorem.
- Matrix_ring wikiPageWikiLink Associative_algebra.
- Matrix_ring wikiPageWikiLink Bicomplex_number.
- Matrix_ring wikiPageWikiLink Biquaternion.
- Matrix_ring wikiPageWikiLink Category:Algebraic_structures.
- Matrix_ring wikiPageWikiLink Category:Matrix_theory.
- Matrix_ring wikiPageWikiLink Category:Ring_theory.
- Matrix_ring wikiPageWikiLink Center_(algebra).
- Matrix_ring wikiPageWikiLink Central_simple_algebra.
- Matrix_ring wikiPageWikiLink Clifford_algebra.
- Matrix_ring wikiPageWikiLink Commutative_ring.
- Matrix_ring wikiPageWikiLink Complex_number.
- Matrix_ring wikiPageWikiLink Diagonal_matrix.
- Matrix_ring wikiPageWikiLink Dimension_(vector_space).
- Matrix_ring wikiPageWikiLink Division_ring.
- Matrix_ring wikiPageWikiLink Endomorphism_ring.
- Matrix_ring wikiPageWikiLink Free_module.
- Matrix_ring wikiPageWikiLink Frobenius_algebra.
- Matrix_ring wikiPageWikiLink General_linear_group.
- Matrix_ring wikiPageWikiLink Generic_matrix_ring.
- Matrix_ring wikiPageWikiLink Group_(mathematics).
- Matrix_ring wikiPageWikiLink Hilbert_space.
- Matrix_ring wikiPageWikiLink Hurwitzs_theorem_(composition_algebras).
- Matrix_ring wikiPageWikiLink Ideal_(ring_theory).
- Matrix_ring wikiPageWikiLink Idempotent_element.
- Matrix_ring wikiPageWikiLink Identity_matrix.
- Matrix_ring wikiPageWikiLink Invertible_matrix.
- Matrix_ring wikiPageWikiLink Involution_(mathematics).
- Matrix_ring wikiPageWikiLink Matrix_(mathematics).
- Matrix_ring wikiPageWikiLink Matrix_addition.
- Matrix_ring wikiPageWikiLink Matrix_multiplication.
- Matrix_ring wikiPageWikiLink Matrix_unit.
- Matrix_ring wikiPageWikiLink Morita_equivalence.
- Matrix_ring wikiPageWikiLink Nilpotent.
- Matrix_ring wikiPageWikiLink Noetherian_ring.
- Matrix_ring wikiPageWikiLink Normed_algebra.
- Matrix_ring wikiPageWikiLink Pauli_matrices.
- Matrix_ring wikiPageWikiLink Prime_ring.
- Matrix_ring wikiPageWikiLink Primitive_ring.
- Matrix_ring wikiPageWikiLink Product_of_rings.
- Matrix_ring wikiPageWikiLink Quaternion.
- Matrix_ring wikiPageWikiLink Real_number.
- Matrix_ring wikiPageWikiLink Ring_(mathematics).
- Matrix_ring wikiPageWikiLink Semiring.
- Matrix_ring wikiPageWikiLink Semisimple_module.
- Matrix_ring wikiPageWikiLink Simple_ring.
- Matrix_ring wikiPageWikiLink Split-biquaternion.
- Matrix_ring wikiPageWikiLink Split-complex_number.
- Matrix_ring wikiPageWikiLink Springer_Science+Business_Media.
- Matrix_ring wikiPageWikiLink Stably_finite_ring.
- Matrix_ring wikiPageWikiLink Subalgebra.
- Matrix_ring wikiPageWikiLink Transpose.
- Matrix_ring wikiPageWikiLink Triangular_matrix.
- Matrix_ring wikiPageWikiLink William_Kingdon_Clifford.
- Matrix_ring wikiPageWikiLink Zero_divisor.
- Matrix_ring wikiPageWikiLinkText "''M''(''n'',''S'')".
- Matrix_ring wikiPageWikiLinkText "M(''n'', ''D'')".
- Matrix_ring wikiPageWikiLinkText "Matrix algebra".
- Matrix_ring wikiPageWikiLinkText "Matrix ring".
- Matrix_ring wikiPageWikiLinkText "full matrix ring".
- Matrix_ring wikiPageWikiLinkText "matrix algebra".
- Matrix_ring wikiPageWikiLinkText "matrix algebras".
- Matrix_ring wikiPageWikiLinkText "matrix ring".
- Matrix_ring wikiPageWikiLinkText "matrix rings".
- Matrix_ring wikiPageWikiLinkText "ring of matrices".
- Matrix_ring wikiPageWikiLinkText "ring of ''n''-by-''n'' matrices".
- Matrix_ring wikiPageWikiLinkText "ring of matrices".
- Matrix_ring wikiPageWikiLinkText "row finite matrices".
- Matrix_ring wikiPageUsesTemplate Template:Citation.
- Matrix_ring wikiPageUsesTemplate Template:Harv.
- Matrix_ring wikiPageUsesTemplate Template:Redirect.
- Matrix_ring subject Category:Algebraic_structures.
- Matrix_ring subject Category:Matrix_theory.
- Matrix_ring subject Category:Ring_theory.
- Matrix_ring comment "In abstract algebra, a matrix ring is any collection of matrices over some ring R that form a ring under matrix addition and matrix multiplication (Lam 1999). The set of n × n matrices with entries from R is a matrix ring denoted Mn(R), as well as some subsets of infinite matrices which form infinite matrix rings. Any subring of a matrix ring is a matrix ring.When R is a commutative ring, the matrix ring Mn(R) is an associative algebra, and may be called a matrix algebra.".
- Matrix_ring label "Matrix ring".
- Matrix_ring sameAs Q2915729.
- Matrix_ring sameAs Maticový_okruh.
- Matrix_ring sameAs Matrizenring.
- Matrix_ring sameAs חוג_מטריצות.
- Matrix_ring sameAs 行列環.
- Matrix_ring sameAs Matrixring.
- Matrix_ring sameAs m.02gf1s.
- Matrix_ring sameAs Q2915729.
- Matrix_ring sameAs 矩阵环.
- Matrix_ring wasDerivedFrom Matrix_ring?oldid=689043570.
- Matrix_ring isPrimaryTopicOf Matrix_ring.