in this note we review a simple criterion, due to ekedahl, for superspecial curves defined over finite fields.using this we generalize and give some simple proofs for some well-known superspecial curves.

If R is a valuation domain of maximal ideal P with a maximal immediate extension of finite rank it is proven that there exists a finite sequence of prime ideals P = L0 ⊃ L1 ⊃ · · · ⊃ Lm ⊇ 0 such that RLj /Lj+1 is almost maximal for each j, 0 ≤ j ≤ m − 1 and RLm is maximal if Lm 6= 0. Then we suppose that there is an integer n ≥ 1 such that each torsion-free R-module of finite rank is a direct s...

The trace of a set F on a another set X is F |X = F ∩ X and the trace of a family F of sets on X is FX = {F |X : F ∈ F}. In this note we prove that if a k-uniform family F ⊂ ([n] k ) has the property that for any k-subset X the trace F|X does not contain a maximal chain (a family C0 ⊂ C1 ⊂ ... ⊂ Ck with |Ci| = i), then |F| ≤ ( n−1 k−1 ) . This bound is sharp as shown by {F ∈ ([n] k ) , 1 ∈ F}. ...

in traditional system of indian medicine, c.bonducella is widely used for its antipyretic, antiperiodic, anticonvulsive, and antiparalytic activities. for assessing anticonvulsant activity, pentylenetetrazole, maximal electro shock, strychnine- and picrotoxin-induced convulsions models were used. diazepam was used as a standard reference for all models except maximal electro shock model, wherei...

This paper studies the behavior of sequences in the maximal ideal space of the algebra of bounded analytic functions on an arbitrary domain. The main result states that for any such sequence, either the sequence has an interpolating subsequence or infinitely many elements of the sequence lie in the same Gleason part. Introduction Fix a positive integer N and fix a nonempty open subset Q. of C ....

The basic notion of the article is a pair (A, U), whereA is a commutative C-algebra and U is a partial isometry such thatA ∋ a → UaU is an endomorphism of A and UU ∈ A. We give a description of the maximal ideal space of the smallest coefficient C-algebra E∗(A) of the algebra C(A, U) generated by the system (A, U).

We prove that every maximal coonitary group has size at least the cardinality of the smallest non{meager set of reals. We also provide a consistency result saying that the spectrum of possible cardinalities of maximal coonitary groups may be quite arbitrary.

Let G denote a locally compact abelian topological group (an l.c.a. group) with dual group C\ We will denote by A7(G) the Banach algebra of bounded regular Borel measures on G under convolution multiplication and by L(G) the algebra of bounded measures absolutely continuous with respect to Haar measure on G (for discussions of these Banach algebras cf. [1], [2], and [5]). In this paper we shall...

‎in this paper‎, ‎the notion of the radical of a filter in‎ ‎residuated lattices is defined and several characterizations of‎ ‎the radical of a filter are given‎. ‎we show that if f is a‎ ‎positive implicative filter (or obstinate filter)‎, ‎then‎ ‎rad(f)=f‎. ‎we proved the extension theorem for radical of filters in residuated lattices‎. ‎also‎, ‎we study the radical‎ ‎of filters in linearly o...

we give a new proof of the well known wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎we apply the concept of frobenius kernel in frobenius representation theorem in finite group‎ ‎theory to build a proof‎.