We provide a construction, refined from an inverse limit, that produces the mod 2 Steenrod and Dyer-Lashof algebras from each other. In fact, the construction relates various subalgebras and quotients of the universal Steenrod algebra of operations for H∞-ring spectra. We also describe how the construction transforms the axiomatic properties of homogeneous pre-Koszul algebras and Poincaré-Birkh...

One of the main virtues of trees is the representation of formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in power series rings. When analyzed in terms of combinatorial Hopf algebras, the simplest examples yield interesting algebraic identities or enumerative...

The algebraic approach to formal language and automata theory is a continuation of the earliest traditions in these fields which had originally strove to find a means of representing languages, translations and other forms of computation by expressions in the same spirit that led to regular expressions; and had originally cast grammars in the role of equational systems over suitably defined alg...

A pre-Lie product is a binary operation whose associator is symmetric in the last two variables. As a consequence its antisymmetrization is a Lie bracket. In this paper we study the symmetrization of the pre-Lie product. We show that it does not satisfy any other universal relation than commutativity. This means that the map from the free commutative-magmatic algebra to the free pre-Lie algebra...

Aim: To evaluate the loss of applied torque (detorque) values in cast and pre-machined abutments for external hex abutment/implant interface of single implant-supported prostheses subjected to mechanical cycling. Methods: Ten metal crowns were fabricated using two types of UCLA abutments: cast and pre-machined with metal base in NiCrTi alloy and tightened to regular external hex implants with a...

We prove that free pre-Lie algebras, when considered as Lie algebras, are free. Working in the category of S-modules, we define a natural filtration on the space of generators. We also relate the symmetric group action on generators with the structure of the anticyclic PreLie operad.

In this paper a strong relation is demonstrated between fork algebras and quasi-projective relation algebras. With the help of the representation theorem of quasi-projective relation algebras, a short proof is given for the representation theorem of fork algebras. Fork algebras, due to their expressive power and applicability in computing science, have been intensively studied in the last four ...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

Let P be any operad. A P-bimodule R that is a P-cooperad induces a natural “fattening” of the category of P-(co)algebras, expanding the morphism sets while leaving the objects fixed. The morphisms in the resulting R-governed category of P-(co)algebras can be viewed as morphisms “up to R-homotopy” of P-(co)algebras. Let A denote the associative operad in the category of chain complexes. We defin...