Injective and projective regular double Stone algebras

We characterize the injective and projective regular double Stone algebras, and describe those regular double Stone algebras which are also projective in the category of double Stone algebras.Presented by Bjarni Jónsson.     

双重Stone代数的主同余关系

给出了双重Stone代数的主同余关系θ(a,b)(a≤b)的等式刻划以及其它的一些性质,由此得到了主同余关系θ(a,b)(a≤b)存在Boo le-补的若干充分条件.     

Perfect extensions of regular double Stone algebras

In 1951 Jónsson and Tarski showed that every Boolean algebra with operators could be embedded in a perfect (or canonical) extension. We obtain a similar result for regular double Stone algebras with operators. As a corollary we obtain another proof that every regular double Stone algebra can be represented as an algebra of rough subsets of an approximation space.Presented by J. Sichler.Research supported in part by The Citadel Development Foundation.     

Endodualisable and endoprimal finite double Stone algebras

The finite endodualisable double Stone algebras are characterised, and every finite endoprimal double Stone algebra is shown to be endodualisable. Received February 24, 1999; accepted in final form May 10, 1999.     

Endodualisable and endoprimal finite double Stone algebras

The finite endodualisable double Stone algebras are characterised, and every finite endoprimal double Stone algebra is shown to be endodualisable. The authors wish to express their gratitude to B. A. Davey and T. Katriňák for their helpful remarks and to J. G. Pitkethly for her assistance with the pictures. A support by Slovak grants VEGA 1/4057/97, 1/3026/06 and APVV-51-009605 is acknowledged by the first author who also wishes to thank the Mathematical Institute of the University of Oxford and the School of Mathematical and Statistical Sciences of La Trobe University for their hospitality.     

Affine complete double Stone algebras with bounded core

Algebra universalis -     

Injective hulls for ordered algebras

We study the injectivity of ordered algebras with respect to the class of homomorphisms that are order-embeddings and one more class of morphisms. We do this in the category where morphisms need not be homomorphisms, but satisfy a condition which is weaker than operation-preservation. In this setting, the injective objects turn out to be precisely sup-algebras. We also show how to construct injective hulls of ordered algebras satisfying certain conditions.     

Affine complete Stone algebras

In [1] R. Beazer characterized affine complete Stone algebras having a smallest dense element. We remove this latter assumption and describe affine complete algebras in the class of all Stone algebras.Dedicated to the memory of M. KolibiarPresented by Á. Szendrei.     

Injective dimension of Weyl algebras over affine coefficient rings

The concern of this paper is to derive formulas for the injective dimension of then- th Weyl algebraA _n (R) in casek is a field of characteristic zero andR is a commutative affinek-algebra of finite injective dimension. For the casen=1 we prove a more general result from which the above result follows. Such formulas can be viewed as generalizations of the corresponding results given by J. C. McConnell in the caseR has finite global dimension.Project supported in part by the National Natural Science Foundation for Youth     

Commuting double Ockham algebras

In this paper,we study a certain class of double Ockham algebras (L;∧,∨,f,k,0,1), namely the bounded distributive lattices (L;∧,∨,0,1) endowed with a commuting pair of unary op- erations f and k,both of which are dual endomorphisms.We characterize the subdirectly irreducible members,and also consider the special case when both (L;f) and (L;k) are de Morgan algebras.We show via Priestley duality that there are precisely nine non-isomorphic subdirectly irreducible members, all of which are simple.