Number theory of matrix semigroups

On upper triangular nonnegative matrices

“…Later, Jacobson and Wisner ( [7], [8]), Chuan and Chuan ( [3], [4]) investigated these factorization problems in the context of semigroups of matrices. Motivated by these results, Baeth et al [2] applied the concepts of contemporary factorization theory to semigroups of integral-valued matrices, and calculated certain important invariants to give an idea of how unique or non unique factorization is in each of these semigroups. In [2], Baeth et al presented six open problems.…”

“…In particular, we investigate the atoms of S, provide a formula for ̺(S), and, given A ∈ S, provide formulas for l(A), L(A) and ̺(A). As a consequence, open problem 4 in [2] is partly answered. In Section 3 we study the semigroup…”

“…Also, some special cases of open problem 2 in [2] are discussed and answered. In Section 4 and 5, we study the upper triangular matrices with positive entries.…”

“…Section 4 investigates some special subsemigroups of T n (N) for n > 2 which are bifurcus, and we compute invariants of such semigroups. Consequently, some special cases of open Problem 3 in [2] are partly answered. In Section 5 we study a special class of matrices in T 2 (N) and also partly answer open Problem 1 in [2].…”

“…Consequently, some special cases of open Problem 3 in [2] are partly answered. In Section 5 we study a special class of matrices in T 2 (N) and also partly answer open Problem 1 in [2].…”