1. Reminder on quotient groups Let G be a group and H a subgroup of G. We have seen that the left cosets xH of H in G give a partition of G. Motivated by the case of quotients of rings by ideals, it is natural to consider the product operation on cosets. Recall that for any subsets S, T of G, by ST we mean {st | s ∈ S, t ∈ T }. If G is commutative, the product of two left cosets is another left...

Let R be a Noetherian domain with finite integral closure R. We study the map from the Brauer group of R, B(R), to B(R): first, by embedding B(R) into the Cech etale cohomology group H (R, U) and using a Mayer-Vietoris sequence for Cech cohomology of commutative rings; second, via Milnor's theorem from algebraic K-theory. We apply our results to show, i.e., that if R is a domain with quotient f...

We build, using the notion of zinbiel algebra, some commutative subalgebras C_{u,v} inside an algebra formal iterated integrals. There is a quotient map from this integrals to motivic multiple zeta values. Restricting gives morphism graded algebras with same dimension. This conjectured be generically isomorphism. When u+v = 0, image instead sub-algebra

Tujuan dari pendidikan kewirausahaan untuk anak usia dini yakni menjadikan peserta didik menjadi orang yang pandai, kreatif dan inovatif sekaligus memiliki jiwa pemberani, suka menerima tantangan, berani mengambil resiko tidak mudah pesimis. Penelitian dilakukan di PAUD TPQ Rochmatul Ummah Purwosari Kudus. Responden dalam penelitian ini adalah ada Kudus dengan tujuan memberikan inovasi kepada s...

We consider countable Borel equivalence relations on quotient Borel spaces. We prove a generalization of the representation theorem of Feldman–Moore, but provide some examples showing that other very simple properties of countable equivalence relations on standard Borel spaces may fail in the context of nonsmooth quotients. In this paper we try to analyze some very basic questions about the str...

We study the quotients of the Toeplitz C*-algebra of a quasi-lattice ordered group (G, P ), which we view as crossed products by a partial actions of G on closed invariant subsets of a totally disconnected compact Hausdorff space, the Nica spectrum of (G, P ). Our original motivation and our main examples are drawn from right-angled Artin groups, but many of our results are valid for more gener...

The quotient of a Boolean algebra by a cyclic group is proven to have a symmetric chain decomposition. This generalizes earlier work of Griggs, Killian and Savage on the case of prime order, giving an explicit construction for any order, prime or composite. The combinatorial map specifying how to proceed downward in a symmetric chain is shown to be a natural cyclic analogue of the sl2 lowering ...

If a Lie group G acts on a symplectic manifold (M, ω) and preserves the symplectic form ω, then in some cases there may exist a moment map ([C]) Φ from M to the dual of the Lie algebra. When the action is (locally) free, the preimage of a point in the dual of the Lie algebra modulo the isotropy group of this point will still be a symplectic manifold (orbifold). This process is called the Marsde...

Azad [1] introduced the concepts of fuzzy semi-open sets and fuzzy semi-continuous mappings. Fuzzy α-open sets and fuzzy α-continuous functions were introduced by Mashhour et. al. [4] and Singal et. al. [6] respectively. The concepts of fuzzy pre-open sets and fuzzy pre-continuous mappings were introduced by Bin Sahana [2]. In this paper the concepts of fuzzy α-quotient maps, fuzzy semi quotien...

We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an expansive quotient of the dynamics and study some dynamical consequences related to this quotient.