Commutative clifford semigroups with maximal endomorphism semirings

For a finite abelian group A, the ring End(A) is a maximal ring in the nearring M(A). In this paper we consider an analogous problem for finite semigroups, concentrating on commutative Clifford semigroups.     

Finite Gröbner basis algebra with unsolvable problem of zero divisors

This work presents a sample construction of an algebra with the ideal of relations defined by a finite Gröbner basis for which the question whether this element is a zero divisor is algorithmically unsolvable. This gives the negative answer to a question raised by V. N. Latyshev.     

On a finite basis problem for universal positive formulas

A finite semigroup without a finite basis of collective identities has been constructed. A semigroup with a finite basis of identities, but without a finite basis of disjunctive identities has been constructed.Presented by B. M. Schein.     

The removability problem for functions with zero spherical means

We study the functions on the punctured n-dimensional sphere having zero integrals over all admissible “hemispheres.” We find a condition for the point to be a removable set for this class of functions and show that the condition cannot be dropped or substantially improved.     

The multiparameter eigenvalue problem: Jordan vector semilattices

In this paper, multiparameter eigenvalue (MPE) problems for matrices are considered. The notion of Jordan vector semilattices as a generalization of the notion of Jordan vector chains is introduced for a multiple spectrum point of disconnected MPE problems. The notion of generating vector is introduced. For the linear case, a special form of equations determining Jordan vector semilattices is presented. The above notions are extended to the case of connected MPE problems, including linear ones. The relationship between the Jordan vector semilattices of a connected linear MPE problem and the Jordan vector chains of the corresponding simultaneous spectral problems for matrices is established. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 219, 1994, pp. 213–220. This paper was supported by the Russian Foundation of Fundamental Research (grant 94-01-00919). Translated by V. B. Khazanov.     

A note on congruences of semilattices with sectionally finite height

We present a bijective correspondence between congruences of semilattices with sectionally finite height (i.e., meet-semilattices whose principal downsets have finite length) and certain special subsets of their universes. We characterize these subsets from a purely order-theoretic point of view and prove that the bijection coincides with the Leibniz operator of abstract algebraic logic.     

On the finite basis problem for certain 2-limited words

Let X* be a free monoid over an alphabet X and W be a finite language over X. Let S(W) be the Rees quotient X*/I(W), where I(W) is the ideal of X* consisting of all elements of X* that are not subwords of W. Then S(W) is a finite monoid with zero and is called the discrete syntactic monoid of W. W is called finitely based if the monoid S(W) is finitely based. In this paper, we give some sufficient conditions for a monoid to be non-finitely based. Using these conditions and other results, we describe all finitely based 2-limited words over a three-element alphabet. Furthermore, an explicit algorithm is given to decide that whether or not a 2-limited word in which there are exactly two non-linear letters is finitely based.     

On semioirect products of two finite semilattices

It is shown that a finite monoid M divides a semidirect product of two finite semilattices iff M satisfies the two following equations: (1) xuyvxy=xuyvyx and (2) xux=xux². The proof rests on language theory and on a theorem of I. Simon on graph congruences. Dedicated to T. Tamura On his 65th Birthday     

The extension problem for functions with zero weighted spherical means

We study functions on a sphere with a pricked point having zero integrals with a given weight over all admissible “hemispheres”. We find a condition under which the point is a removable set for such a class of functions. We show that this condition cannot be dropped or substantially weakened.     

半环的范德瓦尔登问题

首先从半群理论角度解释了整环的分式域过程.其次,给出了构造给定半环的格罗滕迪克环的方法,进一步证明了任意加法可消半环可嵌入其格罗滕迪克环.最后,证明了半环上的同余与其格罗滕迪克环理想之间可以建立一一对应关系.