Order algebras

Multi-Adjoint Algebras Versus Extended-Order Algebras

Adjoint triples are an interesting generalization of t-norms and their residuated implications, since they increase the flexibility in the framework where they are used. Following the same motivation of adjoint triples, in order to reduce the mathematical requirements for the computation, extended-order algebras are studied. Extended-order algebras are implicative algebras that generalize the i...

Higher order peak algebras

Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras (Sym(N))N≥1, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N = 1 and N = 2). We compute their Hilbert series, introduce and study several combinatorial bases, and establish various algebraic identities related to the multisection...

Order Sorted Algebras

In this paper i is a set. Let I be a set, let f be a many sorted set indexed by I, and let p be a finite sequence of elements of I. One can check that f · p is finite sequence-like. Let S be a non empty many sorted signature. A sort symbol of S is an element of S. Let S be a non empty many sorted signature. (Def. 1) An element of the operation symbols of S is said to be an operation symbol of S...

Strictly Order Primal Algebras

Partial orders and the clones of functions preserving them have been thoroughly studied in recent years. The topic of this papers is strict orders which are irreflexive, asymmetric and transitive subrelations of partial orders. We call an algebra A = (A,Ω) strictly order primal if for some strict order (A,<) the term functions are precisely the functions which preserve this strict order. Our ap...

First Order Cohomology of l^1-Munn Algebras and Certain Semigroup Algebras