On some geometrical properties defining classes of rings and varieties of modular lattices

Algebra universalis -     

On some properties of singular matrices

Some results of Ostrowski in [5] are generalized to the case of monotonic norms.     

On some properties of circulant matrices

A class Σ of matrices is studied which contains, as special subclasses, p-circulant matrices (p ? 1), Toeplitz symmetric matrices and the inverses of some special tridiagonal matrices. We give a necessary and sufficient condition in order that matrices of Σ commute with each other and are closed with respect to matrix product.     

On some classes of structured matrices with algebraic trigonometric eigenvalues

Diagonal plus semiseparable matrices are constructed, the eigenvalues of which are algebraic numbers expressed by simple closed trigonometric formulas.     

Combinatorial properties of some classes of matrices over GF(2)

We study several classes of matrices of GF(2) constructed from lists of subsets of finite sets In this paper. We show that all matrices in these classes are representations of connected equicardinal matrix over GF(2). In Matrix terms, these irreducible (defined below) matrices all have the property that every minimal dependent set of column has the same cardinality over GF(2). This fact is shown directly in this paper by elementary matrix considerations. In a subsequent paper, we shall show that these classes of matrices are in fact the classes of canonical forms for all representations of nontrivial binary connected equicardinal matroids.     

On continuity properties of some classes of vector-valued functions

We extend the V BG* property to the context of vector-valued functions and give some characterizations of this property. Necessary and sufficient conditions for vector-valued VBG* functions to be continuous or weakly continuous, except at most on a countable set, are obtained.     

On spectral properties of some classes of linear operators

Voronezh State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 29, No. 2, pp. 61–64, April–June, 1995.     

Correction to combinatiorial properties of some classes of matrices over GF(2)

Due to my oversight in checking the galley proofs, an error has occured in Tran [1]. The wording of proposition 4.2 on page 162 should read.     

On some classes of modules

The aim of this paper is to investigate quasi-corational, comonoform, copolyform and -(co)atomic modules. It is proved that for an ordinal a right R-module M is -atomic if and only if it is -coatomic. And it is also shown that an -atomic module M is quasi-projective if and only if M is quasi-corationally complete. Some other results are developed.     

On some classes of H-semigroups

A semigroup S is called an H-semigroup if every onesided congruence on S is a two-sided congruence on S. In what follows, inverse H-semigroups, t-semisimple inverse H-semigroups and t-semisimple periodic H-semigroups are characterized. A partial characterization of periodic H-semigroups is given and it is shown that every subgroup of an H-semigroup is a Hamiltonian group. In addition, a characterization of finite H-semigroups is obtained using d-products and it is shown that a periodic inverse H-semigroup is the d-product of itsS-subsemigroups, where a d-product and anS-subsemigroups are generalizations of a direct group product and a Sylow subgroup, respectively. These results are part of the author's doctoral dissertation written at The University of Iowa under the supervision of Professor Robert H. Oehmke. Partially supported by ONR Contract N0014-68-A-0500.     

Computing permanents via determinants for some classes of sparse matrices

Starting from recent formulas for calculating the permanents of some sparse circulant matrices, we obtain more general formulas expressing the permanents of a wider class of matrices as a linear combination of appropriate determinants.     

On some classes of nilgroups

Necessary and sufficient conditions for a direct product of connected groups (under the additional assumption that some subsets are nonmeasurable) to be a nilgroup are found.     

Order invariant properties of some matrices

Certain important Toeplitz and composite Toeplitz matrices have order invariant properties. A class of matrices is defined, and a notation for sign patterns of vector and matrix elements is developed which enables some order invariant properties of the matrices to be described. Several examples are given to show how these ideas apply to some important matrices, including those commonly arising from the numerical solution of elliptic partial differential equations. The following information about the inverse of these matrices is obtained: the signs of the elements, the row in which the maximum row sum occurs, and the signs of the elements of the eigenvector corresponding to its dominant eigenvalue.