Let $R$ be an associative ring with unity. An element $x \in R$ is called $\mathbb{Z}G$-clean if $x=e+r$, where $e$ is an idempotent and $r$ is a $\mathbb{Z}G$-regular element in $R$. A ring $R$ is called $\mathbb{Z}G$-clean if every element of $R$ is $\mathbb{Z}G$-clean. In this paper, we show that in an abelian $\mathbb{Z}G$-regular ring $R$, the $Nil(R)$ is a two-sided ideal of $R$ and $\fra...

for 1 ≤ i ≤ m. Suppose that P ⊂ R is a regular prime (R/P is a regular local ring) and 0 6= f ∈ P . The regular local ring R1 = R[ P f ]m where m is a maximal ideal of R[ P f ] containing mR is called a monoidal transform of R. Suppose that V is a valuation ring of the quotient field of S which dominates S (and thus dominates R). Then given a regular prime P of R (or of S) there exists a unique...

We are interested in (ε)-regular bipartite graphs which are the central objects in the regularity lemma of Szemerédi for sparse graphs. A bipartite graph G = (A]B,E) with density p = |E|/(|A||B|) is (ε)-regular if for all sets A′ ⊆ A and B′ ⊆ B of size |A′| ≥ ε|A| and |B ′| ≥ ε|B|, it holds that |eG(A, B′)/(|A′||B′|) − p| ≤ εp. In this paper we prove a characterization for (ε)-regularity. That ...

Let F be a number field, and π an isobaric ([La]), algebraic ([Cl1]) automorphic representation of GLn(AF ). We will call π quasi-regular iff at every archimedean place v of F , the associated n-dimensional representation σv of the Weil group WFv (defined by the archimedean local correspondence) is multiplicity free. For example, when n = 2 and F = Q, a cuspidal π is quasi-regular exactly when ...

We construct integral operators Rr and Hr on a regular q-pseudoconcave CR manifold M such that f = ∂̄MRr(f) + Rr+1(∂̄Mf) +Hr(f), for f ∈ C (0,r) (M) and prove sharp estimates in a special Lipschitz scale.

In this paper we introduce the notion of intuitionistic fuzzy f morphism on intutionistic fuzzy graphs and regular intutionistic fuzzy graph. We study the action of intuitionistic fuzzy f morphism on intuitionistic fuzzy strong regular graphs. We derive some simple but elegent results on weak and coweak isomophisms. Mathematics Subject Classification: 03E72, 03F55

Any two triangulations of a closed surface with the same number of vertices can be transformed into each other by a sequence of flips, provided the number of vertices exceeds a number N depending on the surface. Examples show that in general N is bigger than the minimal number of vertices of a triangulation. The existence of N was known, but no estimate. This paper provides an estimate for N th...

We show the pointwise convergence of averages \[ \mathcal A _N f(x) = \frac {1}{\# {\bf B} _N} \sum _{n \in f(x + n) \] for $f \ell ^1(\mathbb Z )$ where ${\bf \cap [1, N]$, and $ is a $1$-regular sequence i

Let C(α) denote the class of all cardinal sequences of length α associated with compact scattered spaces. Also put Cλ(α) = {f ∈ C(α) : f(0) = λ = min[f(β) : β < α]}. If λ is a cardinal and α < λ++ is an ordinal, we define Dλ(α) as follows: if λ = ω, Dω(α) = {f ∈ {ω, ω1} : f(0) = ω}, and if λ is uncountable, Dλ(α) = {f ∈ {λ, λ} : f(0) = λ, f−1{λ} is < λ-closed and successor-closed in α}. We show...

The study of dihedral f-tilings of the sphere S2 by spherical triangles and equiangular spherical quadrangles (which includes the case of 4-sided regular polygons) was presented in [3]. Also, in [6], the study of dihedral f-tilings of S2 whose prototiles are an equilateral triangle (a 3-sided regular polygon) and an isosceles triangle was described (we believe that the analysis considering scal...