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Keywords: 08B05, 08B10. 2000 Mathematics Subject Classification: 20M18, 08A30.¶Key words and phrases: Inverse semigroup, convex, lattice isomorphism. Basis BL-algebras congruence endomorphism monoid free algebras Key words: Kripke structures, perfect class of Kripke structures, dynamic algebras, algebraic universality. lattice Moufang loops order Paige loops semigroups variety#### Country

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## CURRENTLY DISPLAYING:

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## Monounary algebras and bottleneck algebras

### Algebra Universalis (1998-10-01) 40: 59-72 , October 01, 1998

### Abstract.

This paper deals with representations of monounary algebras by bottleneck algebras (b-representations). Necessary and sufficient conditions for a monounary algebra to have a b-representation are found: In particular, it is shown that each finite monounary algebra is b-representable.

## On lattice-ordered commutative semigroups

### Algebra Universalis (2003-12-01) 50: 341-357 , December 01, 2003

### Abstract.

Decompositions of elements into intersections of primal elements and into intersections
of *p*-components are studied in certain lattice-ordered commutative semigroups, by
making use of the new development in commutative ideal theory without finiteness conditions,
due to Fuchs-Heinzer-Olberding [7]. Several results concerning ideals can be phrased
as theorems in ‘abstract ideal theory’.

The intersections we consider are in general not irredundant, and the associated prime elements are not unique. However, one can establish a canonical intersection that is often irredundant with uniquely determined associated primes.

## On the representation of lattices by subgroup lattices

### Algebra Universalis (1997-01-01) 37: 81-105 , January 01, 1997

### Abstract.

Whitman's condition in a lattice *L* means that, for any elements
$ a, b, c, d \in L, a \wedge b \leq c \vee d $
implies either
$ a \ wedge b \leq c $
or
$ a\wedge b \leq d $
, or
$ a \geq c \vee d $
, or
$ \leq bc \vee d $
. We prove that any lattice satisfying Whitman’s condition can be embedded in the subgroup lattice of a free group of an arbitrary non-soluble group variety. Some interesting corollaries (both on embeddings in lattices of subgroups and others) are examined.

## Algebraic multiplication m-lattices

### Algebra Universalis (2000-10-01) 44: 47-64 , October 01, 2000

## On Flat Semimodules over Semirings

### Algebra Universalis (2004-08-01) 51: 287-299 , August 01, 2004

### Abstract.

The following analog of the characterization of flat modules has been obtained
for the variety of semimodules over a semiring *R: A* semimodule
_{R}*A* is flat (i.e., the tensor
product functor − ⊗ *A* preserves all finite limits) iff
*A* is *L*-flat (i.e., *A*
is a filtered colimit of finitely generated free semimodules). We also give new (homological) characterizations of
Boolean algebras and complete Boolean algebras within the classes of distributive lattices
and Boolean algebras, respectively, which solve two problems left open in [14]. It is also
shown that, in contrast with the case of modules over rings, in general for semimodules over
semirings the notions of flatness and mono-.atness (i.e., the tensor product functor − ⊗ *A*
preserves monomorphisms) are different.

## Flat and weakly flat projection algebras

### Algebra Universalis (2002-12-01) 48: 479-484 , December 01, 2002

### Abstract.

The notion of a projection algebra was first introduced in [4] by Ehrig et al. as an algebraic version of ultrametric spaces. Computer scientists use this notion as a convenient means of algebraic specification of process algebras. Some algebraic notions regarding these algebras have been studied in [1], [2], [5]. The flat projection algebras have been investigated by the authors in [1]. Here we completely characterize flat and weakly flat (*m*-separated and separated) projection algebras.

## Support functions of general convex sets

### Algebra Universalis (2003-09-01) 49: 305-319 , September 01, 2003

### No Abstract.

.

## Internal injectivity of Boolean algebras in MSet

### Algebra Universalis (1999-08-01) 41: 155-175 , August 01, 1999

### Abstract.

This paper deals with the internal notion of injectivity for Boolean algebras in the topos of *M*-sets. Given that, for ordinary Boolean algebraas, injectivity is the same as completeness (Sikorski’s theorem) and the injective hull is the same as normal completion, we investigate here how the *internal* notion of completeness relates to *internal* injectivity. Further, we consider the internal injectivity of the initial Boolean algebra *2* which is equivalent to the prime ideal theorem for Boolean algebras in this topos. Before we turn specificially to Boolean algebras, we develop the bassic general facts concerning internal injectivity in *MSet* for arbitrary equational classes of algebras.

## The probability of triviality

### Algebra Universalis (1997-07-01) 38: 422-449 , July 01, 1997

### Abstract.

Given a variety
$ \cal V $
of algebras, what is the probability that for an arbitrary identity *p*
$ \approx $
*q* the only algebra in
$ \cal V $
that satisfies *p*
$ \approx $
*q* is the trivial algebra? More generally, if
$ \cal W $
is a subvariety of
$ \cal V $
what is the probability that *p*
$ \approx $
*q* together with the identities of
$ \cal V $
forms an equational basis for
$ \cal W $
? We consider these questions for various
$ \cal V $
and
$ \cal W $
and we provide criteria that allow for explicit determination of these probabilities.

## Results on undecidability of isomorphism of forms over polynomial rings

### Algebra Universalis (2003-07-01) 49: 179-189 , July 01, 2003

### Abstract.

We show the undecidability of the question of isomorphism of forms over a
polynomial ring $ R[t_1,\ldots,t_n] $, assuming a hypothesis about units in certain quaternion
rings. Assuming this, it follows that isomorphisms of modules, and of affine algebraic
varieties over *R* are undecidable.