Prime Rings with Involution Equipped with Some New Product

Let R be a ring with involution *. We consider R as a ring equipped with a new product r s = rs + sr^*. The relationship between (ordinary) ideals of R and right ideals of R with respect to the product is studied.AMS Subject Classification (2000): 16W10, 16D25     

Metric and Complete Metric σ-Frames

A -frame is a lattice in which countable joins exist and binary meets distribute over countable joins. In this paper, the category MFrm, of metric -frames, is introduced, and it is shown to be equivalent to the category MLFrm _u, of metric Lindelöf frames.Finally, it is shown that the complete metric -frames are exactly the cozero parts of complete metric Lindelöf frames.     

Induced product representations of extended Cuntz algebras

Let _H be the extended Cuntz algebra over the Hilbert space H. Since its zero grade part _H⁰ is the C^*-inductive limit of B(H^r), we look for some family of representations on an inductive limit of H^r as r. When such construction is shaped according to the structure of _H⁰, von Neumanns notion of a reference sequence of unit vectors for Hilbert infinite tensor products emerges; after a further Rieffel induction step, a class IPR[H] of representations of _H arises. For any two such representations, we describe explicitly their associated intertwiners. Any two representations in IPR[H] are either disjoint or unitarily equivalent. Actions of the group by translation on sequences of unit vectors are involved, as well as the ideals of .     

Initial Segments in Rogers Semilattices of \Sigma _n^0 -Computable Numberings

S. Goncharov and S. Badaev showed that for , there exist infinite families whose Rogers semilattices contain ideals without minimal elements. In this connection, the question was posed as to whether there are examples of families that lack this property. We answer this question in the negative. It is proved that independently of a family chosen, the class of semilattices that are principal ideals of the Rogers semilattice of that family is rather wide: it includes both a factor lattice of the lattice of recursively enumerable sets modulo finite sets and a family of initial segments in the semilattice of -degrees generated by immune sets.     

Orders on Braid Groups

It is shown that the braid group defies lattice ordering.     

On the Operator Semirings of a Γ-Semiring

In this paper we introduce the notion of operator semirings of a -semiring to study -semirings. It is shown that the lattices of all left (right) ideals (two-sided ideals) of a -semiring and its right (respectively left) operator semiring are isomorphic. This has many applications to characterize various -semirings.AMS Subject Classification (2000): 16Y60, 16Y99     

Flow Compactifications of Nondiscrete Monoids, Idempotents and Hindman's Theorem

We describe the extension of the multiplication on a not-necessarily-discrete topological monoid to its flow compactification. We offer two applications. The first is a nondiscrete version of Hindman's Theorem, and the second is a characterization of the projective minimal and elementary flows in terms of idempotents of the flow compactification of the monoid.     

Iterated monoidal categories

We develop a notion of an n-fold monoidal category and show that it corresponds in a precise way to the notion of an n-fold loop space. Specifically, the group completion of the nerve of such a category is an n-fold loop space, and free n-fold monoidal categories give rise to a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an n-fold loop space. We also show directly that this operad has the same homotopy type as the n-th Smith filtration of the Barratt-Eccles operad and the n-th filtration of Berger's complete graph operad. Moreover, this operad contains an equivalent preoperad which gives rise to Milgram's small model for when n=2 and is very closely related to Milgram's model of for n>2.     

On the commutator of the Marcinkiewicz integral

boundedness is considered for the commutator of higher-dimensional Marcinkiewicz integral. Some conditions implying the and the boundedness for the commutator of the Marcinkiewicz integral are obtained.     

Fluctuation-dominated kinetics in the a+b→0 reaction between immobile particles

We consider the accumulation of immobile particles landing on a one-dimensional lattice and annihilating via the A + B 0 bimolecular reaction. Here we focus on short-range interactions with cutoff. We investigate through computer simulations both the kinetics of the particles' accumulation and also their spatial distribution. The relation between the exponents describing the growth of the particles' concentration and the correlation length of their distribution shows that the kinetics of accumulation is fluctuation-dominated.This work is dedicated to Prof. George H. Weiss.