Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

We consider a generalization E(n) of the Johnson-Wilson spectrum E(n) for which E(n)∗ is a local ring with maximal ideal In. We prove that the spectra E(n), E(n) and Ê(n) are Bousfield equivalent. We also show that the Hopf algebroid E(n)∗E(n) is a free E(n)∗-module, generalizing a result of Adams and Clarke for KU∗KU . 1991 Mathematics Subject Classification: Primary 55N20 55N22

At the beginning of the last century F. S. Macaulay developed an elegant theory (see [4] Part IV) describing homogeneous ideals in polynomial rings. This theory makes the maximal-primary irriducible ideals I ⊂ Fýz1 , . . . , znü correspond to a single homogeneous inverse polynomial θI ∈ Fýz−1 1 , . . . , z−1 n ü. Macaulay’s theory has recently attracted attention in connection with problems ari...

‡ Every function on a finite residue class ring D/I of a Dedekind domain D is induced by an integer-valued polynomial on D that preserves congruences mod I if and only if I is a power of a prime ideal. If R is a finite commutative local ring with maximal ideal P of nilpotency N satisfying for all a, b∈R, if ab∈ P then a∈ P k , b∈ P j with k+ j ≥min(n,N), we determine the number of functions (as...

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...

We study the structure of the maximal ideal space M(H∞) of the algebra H ∞ = H∞(D) of bounded analytic functions defined on the open unit disk D ⊂ C. Based on the fact that dim M(H∞) = 2 we prove for H∞ the matrix-valued corona theorem. Our results heavily rely on the topological construction describing maximal ideal spaces of certain algebras of continuous functions defined on the covering spa...