We prove that left cancellative right hereditary monoids satisfying the dedekind height property are precisely the Zappa-Szép products of free monoids and groups. The ‘fundamental’ monoids of this type are in bijective correspondence with faithful self-similar group actions. 2000 AMS Subject Classification: 20M10, 20M50. 1 A class of left cancellative monoids This paper develops some ideas that...

0. Introduction. The literature on algebraic semigroups contains publications concerning two distinct types of semigroup extensions. Ideal extensions of semigroups were introduced by Clifford in [1] whereas Rédei [9] introduced Schreier extensions of monoids (a monoid is a semigroup containing an identity element). Let A and 5 be two disjoint semigroups and let 5" contain a zero element o. A se...

[1] The rare earth elements (REEs) with their systematically varying properties are powerful tracers of continental inputs, particle scavenging intensity and the oxidation state of seawater. However, their generally low ( pmol/kg) concentrations in seawater and fractionation potential during chemical treatment makes them difficult to measure. Here we report a technique using an automated precon...

The concept of semi-regular sets of matrices was introduced by J. Seberry in "A new construction for Williamson-type matrices", Graphs and Combinatorics, 2(1986), 81-87. A regular s-set of matrices of order m was first discovered by J. Seberry and A. L. Whiteman in "New Hadamard matrices and conference matrices obtained via Mathon's construction", Graphs and Combinatorics, 4(1988), 355-377. In ...

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The semigroup of binary relations on {1, . . . , n} with the relative product is isomorphic to the semigroup Bn of n×n matrices over {0, 1} with the Boolean matrix product. Over any field F , we prove that there is an ideal Kn in FBn of dimension (2n−1)2, and we construct an explicit isomorphism of Kn with the matrix algebra M2n−1(F ). Let Zn = {1, . . . , n} (n ≥ 1); then P (Z n), the power se...

In this paper we study decidability and complexity of decision problems on matrices from the special linear group SL(2,Z). In particular, we study the freeness problem: given a finite set of matrices G generating a multiplicative semigroup S, decide whether each element of S has at most one factorization over G. In other words, is G a code? We show that the problem of deciding whether a matrix ...