An example of a nitely presented monoid is given that does not satisfy the homo-topical niteness condition FHT, although it satisses both the homological niteness conditions left FP 1 and right FP 1 .tions left FP 1 and right FP 1 .

We prove that given a finite (zero) exact right decomposition (M, T ) of a semigroup S, if M is defined by a finite complete presentation then S is also defined by a finite complete presentation. Exact right decompositions are natural generalizations to semigroups of coset decompositions in groups. As a consequence we deduce that the Zappa-Szép extension of a monoid defined by a finite complete...

Let R be a ring and C a class of right R-modules closed under finite direct sums. If we suppose that C has a set of representatives, that is, a set V(C) ⊆ C such that every M ∈ C is isomorphic to a unique element [M ] ∈ V(C), then we can view V(C) as a monoid, with the monoid operation [M1] + [M2] = [M1 ⊕M2]. Recent developments in the theory of commutative monoids (e.g., [4], [15]) suggest tha...

Given an n n table of a cancellative operation on a domain of size n, we investigate the complexity of determining whether is close (equal on most pairs of inputs) to an associative, commutative, and cancellative group operation 0. We show that one can perform such a test in O(n) time. In contrast, quadratic time is necessary and sufficient to test that a given operation is cancellative, associ...

In this paper we study a class of infinite words on a finite alphabet A whose factors are closed under the image of an involutory antimorphism θ of the free monoid A∗. We show that given a recurrent infinite word ω ∈ AN, if there exists a positive integer K such that for each n ≥ 1 the word ω has 1) cardA + (n − 1)K distinct factors of length n, and 2) a unique right and a unique left special f...

We use information theory to study recovering sets RL and strongly cancellative sets CL on different lattices. These sets are special classes of recovering pairs and cancellative sets previously discussed in the papers of Simonyi, Frankl, and Füredi. We mainly focus on the lattices Bn and D k l . Specifically, we find upper bounds and constructions for the sets RBn , CBn , and CDk l .

Z. Feng and R.W. Heath proved that any separable linearly ordered space (LOTS) which is a cancellative topological semigroup must be metrizable. In this note, we show that the same holds more generally for CCC LOTS by proving that no Souslin line admits a continuous cancellative binary operation. We also show that no Lindelöf Aronszajn line admits such an operation.

The main result of the work “The nilpotence conjecture in K-theory of toric varieties” is extended to all coefficient fields of characteristic 0, thus covering the class of genuine toric varieties. 1. The statement Let R be a (commutative) regular ring, M be arbitrary commutative, cancellative, torsion free monoid without nontrivial units, and i be a nonnegative integral number. The nilpotence ...