Number theory of matrix semigroups

DOI10.1016/j.laa.2010.09.028zbMath1250.11104OpenAlexW2001357556MaRDI QIDQ616404

Sumit K. Garg

Publication date: 7 January 2011

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2010.09.028

zbMATH Keywords

factorizationmatrix semigroupsintegral-valued matrices

Mathematics Subject Classification ID

Factorization of matrices (15A23) Matrices of integers (15B36) Factorization; primality (11A51) Semigroups (20M99) Matrices, determinants in number theory (11C20)

Related Items (17)

On length densities ⋮ Semigroups of non-negative integer-valued matrices ⋮ Factorizations of block triangular matrices ⋮ Non-commutative Krull monoids: a divisor theoretic approach and their arithmetic. ⋮ Upper triangular matrices over information algebras ⋮ The Importance of Being Prime ^⋆ , a Nontrivial Generalization for Nonunique Factorizations ⋮ Factorization in additive monoids of evaluation polynomial semirings ⋮ Factorizations of upper triangular matrices ⋮ On factorizations of upper triangular nonnegative matrices of order three ⋮ Factorizations in Bounded Hereditary Noetherian Prime Rings ⋮ Factorization theory: from commutative to noncommutative settings. ⋮ Nonunique factorization over quotients of PIDs ⋮ Arithmetic of seminormal weakly Krull monoids and domains ⋮ Factorizations of Elements in Noncommutative Rings: A Survey ⋮ On upper triangular nonnegative matrices ⋮ THE CATENARY DEGREE OF KRULL MONOIDS II ⋮ Isomorphism in wavelets

Cites Work

• On similarity of second order matrices over the ring of integers
• Bifurcus semigroups and rings.
• Factorization in hereditary orders
• Partial orderings for sets of multisets
• Separability of distinct Boolean rank-1 matrices
• On Markov's undecidability theorem for integer matrices.
• Factorizations in a semigroup of integral matrices
• Nonunique Factorization in Subsemigroups of Semigroups with Unique Prime Factorization
• Rank and perimeter preserver of rank-1 matrices over max algebra
• ON THE KROHN–RHODES COMPLEXITY OF SEMIGROUPS OF UPPER TRIANGULAR MATRICES
• Matrix Number Theory: An Example of Nonunique Factorization
• Presentations of the Schützenberger Product of n Groups
• Noncommutative Unique Factorization Domains
• Approximation of real matrices by integral matrices
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