35 citations · 254 across the 32 of their papers we have counts for
34 papers
Zhang twists for semigroups and groupoids, with applications to Steinberg algebras
Roozbeh Hazrat, Zachary Mesyan, Benjamin Steinberg
Zhang twists provide a powerful mechanism for deforming graded algebras, while preserving their graded module categories. We extend this theory by introducing Zhang twists for grad…
Graded Lawson-Stone Duality
Roozbeh Hazrat, Zachary Mesyan
The classical Stone duality associates to each Boolean algebra a topological space consisting of ultrafilters. Lawson's generalisation constructs a dual equivalence of categories o…
Factorization in Finitely-Presented Monoids
Alfred Geroldinger, Zachary Mesyan
We study arithmetic properties of factorizations of elements into products of generators, in monoids given with explicit presentations. After relating and comparing this perspectiv…
Maximal Commutative Subalgebras of Steinberg Algebras
Anna Cichocka, Zachary Mesyan, Michal Ziembowski
We construct large classes of maximal commutative subalgebras in prime Steinberg algebras, generalizing a known result for Leavitt path algebras.
Conjugacy and Least Commutative Congruences in Semigroups
Zachary Mesyan
Given a semigroup and , write if and , for some . This relation, known as "primary conjugacy", along with its trans…
Unifying some classical results on Artinian rings and modules
Donovan Leyba, Zachary Mesyan, Greg Oman
In this note, we introduce a very crude but natural notion of measure on the class of left R-modules over a ring R. We use this notion to give short proofs of some classical theore…
Properties of Congruence Lattices of Graph Inverse Semigroups
Marina Anagnostopoulou-Merkouri, Zak Mesyan, James D. Mitchell
From any directed graph one can construct the graph inverse semigroup , whose elements, roughly speaking, correspond to paths in . Wang and Luo showed that the congrue…
Products and Intersections of Prime-Power Ideals in Leavitt Path Algebras
Zachary Mesyan, Kulumani M. Rangaswamy
We continue a very fruitful line of inquiry into the multiplicative ideal theory of an arbitrary Leavitt path algebra L. Specifically, we show that factorizations of an ideal in L…
Graded Semigroups
Roozbeh Hazrat, Zachary Mesyan
We systematically develop a theory of graded semigroups, that is semigroups S partitioned by groups G, in a manner compatible with the multiplication on S. We define a smash produc…
Automatic continuity, unique Polish topologies, and Zariski topologies on monoids and clones
L. Elliott, J. Jonušas, Z. Mesyan +3
In this paper we explore the extent to which the algebraic structure of a monoid determines the topologies on that are compatible with its multiplication. Specifically we s…
Products of Ideals in Leavitt Path Algebras
Gene Abrams, Zachary Mesyan, Kulumani M. Rangaswamy
Ideals in Leavitt path algebras have been shown to share many properties with those of integral domains. Since studying factorizations of ideals in integral domains into special ty…
Topological Transformation Monoids
Z. Mesyan, J. D. Mitchell, Y. H. Péresse
We investigate semigroup topologies on the full transformation monoid T(X) of an infinite set X. We show that the standard pointwise topology is the weakest Hausdorff semigroup top…
Infinite-Dimensional Triangularizable Algebras
Zachary Mesyan
Let End(V) denote the ring of all linear transformations of an arbitrary k-vector space V over a field k. We define a subset X of End(V) to be "triangularizable" if V has a well-or…
Chains of Semiprime and Prime Ideals in Leavitt Path Algebras
Gene Abrams, Be'eri Greenfeld, Zachary Mesyan +1
Semiprime ideals of an arbitrary Leavitt path algebra L are described in terms of their generators. This description is then used to show that the semiprime ideals form a complete…
An infinite cardinal-valued Krull dimension for rings
K. Alan Loper, Zachary Mesyan, Greg Oman
We define and study two generalizations of the Krull dimension for rings, which can assume cardinal number values of arbitrary size. The first, which we call the "cardinal Krull di…
Infinite-Dimensional Triangularization
Zachary Mesyan
The goal of this paper is to generalize the theory of triangularizing matrices to linear transformations of an arbitrary vector space, without placing any restrictions on the dimen…
Realizing posets as prime spectra of Leavitt path algebras
Gene Abrams, Gonzalo Aranda Pino, Zachary Mesyan +1
We associate in a natural way to any partially ordered set a directed graph (where the vertices of correspond to the elements of , and the edges of …
Traces on Semigroup Rings and Leavitt Path Algebras
Zachary Mesyan, Lia Vas
The trace on matrix rings, along with the augmentation map and Kaplansky trace on group rings, are some of the many examples of linear functions on algebras that vanish on all comm…
Infinite-dimensional diagonalization and semisimplicity
Miodrag C. Iovanov, Zachary Mesyan, Manuel L. Reyes
We characterize the diagonalizable subalgebras of End(V), the full ring of linear operators on a vector space V over a field, in a manner that directly generalizes the classical th…
The Structure of a Graph Inverse Semigroup
Zachary Mesyan, J. D. Mitchell
Given any directed graph E one can construct a graph inverse semigroup G(E), where, roughly speaking, elements correspond to paths in the graph. In this paper we study the semigrou…
Topological Graph Inverse Semigroups
Z. Mesyan, J. D. Mitchell, M. Morayne +1
To every directed graph one can associate a \emph{graph inverse semigroup} , where elements roughly correspond to possible paths in . These semigroups generalize polyc…
Polynomials of small degree evaluated on matrices
Zachary Mesyan
A celebrated theorem of Shoda states that over any field K (of characteristic 0), every matrix with trace 0 can be expressed as a commutator AB-BA, or, equivalently, that the set o…
Commutator Leavitt path algebras
Zachary Mesyan
For any field K and directed graph E, we completely describe the elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E),L_K(E)]. We then use this…
The Bergman-Shelah Preorder on Transformation Semigroups
Z. Mesyan, J. D. Mitchell, M. Morayne +1
Let $\nat^\nat$ be the semigroup of all mappings on the natural numbers $\nat$, and let and be subsets of $\nat^\nat$. We write if there exists a countabl…