Rings and semigroups with permutable zero products

Zero-divisor Graphs of Finite Direct Products of Finite Non-commutative Rings and Semigroups

We determine the number of edges of the zero-divisor graph of the direct product of finitely many finite non-commutative rings or semigoups.

Infinite Products of Zero-dimensional Commutative Rings

Semigroups , Rings , and Markov

We analyze random walks on a class of semigroups called \left-regular bands". These walks include the hyperplane chamber walks of Bidi-gare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are diagonalizable and we calculate the eigenvalues and multiplicities. The methods lead to explicit formulas for the projections onto the eigenspaces. As examples of ...

Zero-One Law for Regular Languages and Semigroups with Zero

A regular language has the zero-one law if its asymptotic density converges to either zero or one. We prove that the class of all zero-one languages is closed under Boolean operations and quotients. Moreover, we prove that a regular language has the zero-one law if and only if its syntactic monoid has a zero element. Our proof gives both algebraic and automata characterisation of the zero-one l...

Semigroups, Rings, and Markov Chains

We analyze random walks on a class of semigroups called ``left-regular bands.'' These walks include the hyperplane chamber walks of Bidigare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are diagonalizable and we calculate the eigenvalues and multiplicities. The methods lead to explicit formulas for the projections onto the eigenspaces. As examples of...