Related papers: Betti elements and full atomic support in rings an…
For a continuous angle-valued map defined on a compact ANR, a fixed field and any degree one proposes a refinement of the Novikov-Betti number and of the Novikov homology of the pair consisting of the ANR and the degree one integral…
Let A be an associative algebra with identity over a field k. An atomistic subsemiring R of the lattice of subspaces of A, endowed with the natural product, is a subsemiring which is a closed atomistic sublattice. When R has no zero…
In this paper we develop a new technique to compute the Betti table of a monomial ideal. We present a prototype implementation of the resulting algorithm and we perform numerical experiments suggesting a very promising efficiency. On the…
This paper is concerned with generalising the results for Lie $CT$-algebras to Leibniz algebras. In some cases our results give a generalisation even for the case of a Lie algebra. Results on $A$-algebras are used to show every Leibniz…
We complete the classification of algebraic monoid structures on the affine 3-space. The result is based on a reduction of the general case to that of commutative monoids. We also study various algebraic properties of all monoids appearing…
We prove an analogue of the Approximation Theorem of L^2-Betti numbers by Betti numbers for arbitrary coefficient fields and virtually torsionfree amenable groups. The limit of Betti numbers is identified as the dimension of some module…
We give a precise description of how the class group of a number field measures the failure of unique factorization in its ring of integers. Specifically, following ideas of Kummer, we determine the structure of all irreducible…
Bar Codes are combinatorial objects encoding many properties of monomial ideals. In this paper we employ these objects to study Janet-like divisions. Given a finite set of terms U, from its Bar Code we can compute the Janet-like…
Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…
The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…
In algebra, atomicity is the study of divisibility by and factorizations into atoms (also called irreducibles). In one side of the spectrum of atomicity we find the antimatter algebraic structures, inside which there are no atoms and,…
Let $M$ be a commutative cancellative monoid. The set $\Delta(M)$, which consists of all positive integers which are distances between consecutive factorization lengths of elements in $M$, is a widely studied object in the theory of…
It is known that the numerical invariants Betti numbers and Bass numbers are worthwhile tools for decoding a large amount of information about modules over commutative rings. We highlight this fact, further, by establishing some criteria…
We generalize the constructions of [17,19] to layered semirings, in order to enrich the structure and provide finite examples for applications in arithmetic (including finite examples). The layered category theory of [19] is extended…
The aim of this paper is to solve a problem proposed by Dominique Bourn: to provide a categorical-algebraic characterisation of groups amongst monoids and of rings amongst semirings. In the case of monoids, our solution is given by the…
Multifraction reduction is a new approach to the word problem for Artin-Tits groups and, more generally, for the enveloping group of a monoid in which any two elements admit a greatest common divisor. This approach is based on a rewrite…
We study algebraic structures of certain submonoids of the monoid of homology cylinders over a surface and the homology cobordism groups, using Reidemeister torsion with non-commutative coefficients. The submonoids consist of ones whose…
In this paper, we give the necessary and sufficient conditions for the Cohen-Macaulayness of the associated graded ring of a simplicial affine semigroups using Gr\"{o}bner basis. We generalize the concept of homogeneous numerical semigroup…
The theory of finitely supported algebraic structures represents a reformulation of Zermelo-Fraenkel set theory in which every construction is finitely supported according to the action of a group of permutations of some basic elements…
We introduce and study a derived version $\mathbf L\mathrm{Bin}$ of the binomial monad on the unbounded derived category $\mathscr D(\mathbb Z)$ of $\mathbb Z$-modules. This monad acts naturally on singular cohomology of any topological…