We aim to reconstruct a monoid scheme X from the category of quasi-coherent sheaves over it. This is much in vein Gabriel's original reconstruction theorem. Under some finiteness condition on schemes X, we show that localisations topos Qc(X) are one-to-one correspondence with open subsets while elements correspond points Qc(X). allows us

Tall–Wraith monoids were introduced in [SW09] to describe the algebraic structure on the set of unstable operations of a suitable generalised cohomology theory. In this paper we begin the study of Tall–Wraith monoids in an algebraic and categorical setting. We show that forV a variety of algebras, applying the freeV-algebra functor to a monoid in Set produces a Tall–Wraith monoid. We also study...

We consider the value 1 problem for probabilistic automata over finite words. This problem is known to be undecidable. However, different algorithms have been proposed to partially solve it. The aim of this paper is to prove that one such algorithm, called the Markov Monoid algorithm, is optimal. To this end, we develop a profinite theory for probabilistic automata. This new framework gives a t...

This paper concerns residuated lattice-ordered idempotent commutative monoids that are subdirect products of chains. An algebra of this kind is a generalized Sugihara monoid (GSM) if it is generated by the lower bounds of the monoid identity; it is a Sugihara monoid if it has a compatible involution ¬. Our main theorem establishes a category equivalence between GSMs and relative Stone algebras ...

Pursuing ideas of Jeff Smith, we develop a homotopy theory of ideals of monoids in a symmetric monoidal model category. This includes Smith ideals of structured ring spectra and of differential graded algebras. Such Smith ideals are NOT subobjects, and as a result the theory seems to require us to consider all Smith ideals of all monoids simultaneously, rather then restricting to the Smith idea...

Introduction. It is undecidable whether a monoid given by a nite presentation is nite (see, e.g., [1], pp. 157{160). On the other hand, with the mere knowledge that the monoid is nite, one can e ectively construct the multiplication table of the monoid, and thus obtain a complete understanding of its structure. This paper will present this construction method in detail (Section 2) and o er some...

An original digital signature scheme based on action of infinite ring on module is presented. It is assumed that the ring contains an infinite multiplicative monoid. The ring action is defined as monoid elements's action on the module element as an operator. The signature scheme is based on particularly designed one–way functions (OWFs), using a postulated hard problem in monoid action level. T...

For a monoid M , we introduce linear M-Armendariz rings, which are generalization of M-Armendariz rings and linear Armendariz rings; and investigate their properties. Every reduced ring is linear M-Armendariz, for any unique product monoid. We show that if M be a monoid and R be a right ore ring with classical right quotient ring Q. Then R is linear M-Armendariz if and only if Q is linear M-Arm...

A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show how to directly read several properties of the associated monoid and group from a complete presentation: cancellativity or existence of common multiples in the...