We show that, for an arbitrary graph, a regular ideal of the associated Leavitt path algebra is also graded. As consequence, row-finite we obtain that quotient by again and Condition (L) preserved quotients ideals. Furthermore, describe vertex set make comparison between theory ideals in algebras graph C*-algebras.

in this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. we characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. we also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.

We show that there are $2^{2^{\aleph_0}}$ different closed ideals in the Banach algebra $L(L_p(0,1))$, $1<p\not= 2<\infty$. This solves a problem A. Pietsch's 1978 book Operator Ideals. The proof is quite from other methods of producing space bounded operators on space; particular, not contained strictly singular and yet do contain projections onto subspaces non Hilbertian. give criterion for w...

In discrete convex analysis, the scaling and proximity properties for the class of L-convex functions were established more than a decade ago and have been used to design efficient minimization algorithms. For the larger class of integrally convex functions of n variables, we show here that the scaling property only holds when n ≤ 2, while a proximity theorem can be established for any n, but o...

In a series of papers, Brzozowski together with Tamm, Davies, and Szyku la studied the quotient complexities of atoms of regular languages [6, 7, 3, 4]. The authors obtained precise bounds in terms of binomial sums for the most complex situations in the following five cases: (G): general, (R): right ideals, (L): left ideals, (T ): two-sided ideals and (S): suffix-free languages. In each case le...

In a commutative f-ring, an 1-ideal I is called pseudoprime if ab = 0 implies a E I or b E I, and is called square dominated if for every a E I, lal < x2 for some x E A such that x2 E I. Several characterizations of pseudoprime 1-ideals are given in the class of commutative semiprime frings in which minimal prime 1-ideals are square dominated. It is shown that the hypothesis imposed on the f-ri...

Let S be a finite set of n points in the plane in general position. A k-hole of S is a simple polygon with k vertices from S and no points of S in its interior. A simple polygon P is l-convex if no straight line intersects the interior of P in more than l connected components. Moreover, a point set S is l-convex if there exists an l-convex polygonalization of S. Considering a typical Erdős-Szek...