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...

A function on an algebra is congruence preserving if, for any congruence, it maps congruent elements to congruent elements. We show that, on a free monoid generated by at least three letters, a function from the free monoid into itself is congruence preserving if and only if it is of the form x 7→ w0xw1 · · ·wn−1xwn for some finite sequence of words w0, . . . , wn. We generalize this result to ...

We study formulas for Fibonacci numbers as sums over compositions. The Fibonacci number Fn+1 is the number of compositions of n with parts 1 and 2. Compositions with parts 1 and 2 form a free monoid under concatenation, and our formulas arise from free submonoids of this free monoid.

Cet article pr esente une etude combinatoire du mono de Chinois, un mono de ternaire proche du mono de plaxique, fond e sur le sch ema cba bca cab. Un algo-rithme proche de l'algorithme de Schensted nous permet de caract eriser les classes d' equivalence et d'exhiber une section du mono de. Nous enonn cons egalement une correspondance de Robinson-Schensted pour le mono de Chinois avant de nous ...

We study properties of the forgotten monoid which appeared in work of Lascoux and Schützenberger and recently resurfaced in the construction of dual equivalence graphs by Assaf. In particular, we provide an explicit characterization of the forgotten classes in terms of inversion numbers and show that there are n − 3n + 4 forgotten classes in the symmetric group Sn. Each forgotten class contains...