1. Ideales binomiales y aplicaciones - Ojeda Martínez de Castilla, Ignacio
Edición digital a partir del texto original de la tesis doctoral.

2. Rough Relation Algebras - Relation Algebras
: Rough relation algebras were introduced by S. Comer as a generalisation of algebras of Pawlak 's rough sets and Tarski's relation algebras. In this paper, some algebraic and arithmetical properties of rough relation algebras are studied and the representable rough relation algebras are characterised. 1. Definitions and preliminary results We assume that the reader is familiar with the basic facts of relation algebras as presented e.g. in [4] or [8]. For Stone algebras the reader is invited to consult [2]. Rough sets and rough relations were introduced by Z. Pawlak ([10], [11]) arising from his work on approximation spaces and information systems, and presented as an...

3. Rough Relation Algebras - Rough Relation Algebras
: Rough relation algebras were introduced by S. Comer as a generalisation of algebras of Pawlak 's rough sets and Tarski's relation algebras. In this paper, some algebraic and arithmetical properties of rough relation algebras are studied and the representable rough relation algebras are characterised. 1. Definitions and preliminary results We assume that the reader is familiar with the basic facts of relation algebras as presented e.g. in [4] or [8]. For Stone algebras the reader is invited to consult [2]. Rough sets and rough relations were introduced by Z. Pawlak ([10], [11]) arising from his work on approximation spaces and information systems, and presented as an...

4. Rough Relation Algebras - Relation Algebras,Ivo Dntsch
: Rough relation algebras were introduced by S. Comer as a generalisation of algebras of Pawlak 's rough sets and Tarski's relation algebras. In this paper, some algebraic and arithmetical properties of rough relation algebras are studied and the representable rough relation algebras are characterised. 1. Definitions and preliminary results We assume that the reader is familiar with the basic facts of relation algebras as presented e.g. in [4] or [8]. For Stone algebras the reader is invited to consult [2]. Rough sets and rough relations were introduced by Z. Pawlak ([10], [11]) arising from his work on approximation spaces and information systems, and presented as an...

5. Identidades polinomiais em algebras - Ednei Aparecido Santulo Junior
Apresentamos aqui os conceitos introdutórios à teoria de PI-álgebras, bem como apresentamos resultados que forneceram, ao longo da história, ferramentas poderosas para lidar com PI-álgebras sobre corpos de característica nula. Além disso, exibimos uma base para o conjunto de identidades polinomiais da álgebra de Grassmann, e por fim, mostramos que o teorema de Kemer sobre o produto de álgebras T-primas falha ao trabalharmos com corpos de característica positiva

6. Maximal MV-algebras - Filipoiu, A.; Georgescu, George; Lettieri, Ada
In this paper we define maximal MV-algebras, a concept similar to the maximal rings and maximal distributive lattices. We prove that any maximal MV-algebra is semilocal, then we characterize a maximal MV-algebra as finite direct product of local maximal MV-algebras.

7. On a characterization of Azumaya algebras - Dicks McLay, Warren
A direct proof of Braun's characterization of Azumaya algebras is given.

8. Homotopy Batalin-Vilkovisky algebras - Gálvez-Carrillo, Maria Immaculada; Tonks, Andrew; Vallette, Bruno
This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defined by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincaré-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of...

9. Discontinuity of the product in multiplier algebras - Oudadess, M.
Entire functions operate in complete locally A-convex algebras but not continuously. Actually squaring is not always continuous. The counterexample we give is multiplier algebra.

10. -Algebras - Claus Hintermeier
intervals on them. Example 1. Consider the following specification in pseudo-OBJ syntax, where we distinguish between capital and small letters: obj NATS kind Nats sorts zero : -? Nats succ : Nats -? Nats sort-var X :: Nats ops 0 : -? zero s : X -? succ(X). In the initial algebra of this specification, which is unique up to isomorphism, succ n (zero) is interpreted as singleton fs n (0)g and Nats is the set of all such singletons. Now intervals on natural numbers can be specified as follows: obj INATS kind INats import NATS sorts leq : Nats -? INats geq : Nats -? INats between :Nats Nats -? INats sort-var X,Y :: Nats subsorts X ! leq(X) ! leq(succ(X)) X ! geq(X)...

11. Stable rank of leavitt path algebra - Pardo, E.; Ara i Bertrán, Pere
We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.

12. Strategy and Prosody in Listening to Algebra - Robert Stevens Peter; Peter Wright; Alistair Edwards
The work reported here was part of research into the design of the Mathtalk program. This allows visually disabled people to read algebra notation using synthetic speech and non-speech audio [7]. This paper describes an experiment that investigated the problems of reading algebra notation by listening. The two questions addressed in this paper are firstly, does using prosodic cues facilitate the process of reading by listening and secondly, what is the role of external memory. Keywords: Algebra, Visually disabled readers, Prosody, External memory, Information reduction Introduction The work reported here was part of research into the design of the Mathtalk...

13. Solving equations over small unary algebras - Przemyslaw Broniek
We consider the problem of solving a system of polynomial equations over fixed algebra A which we call MPOLSAT(A). We restrict ourselves to unary algebras and give a partial characterization of complexity of MPOLSAT(A). We isolate a preorder P(A) to show that when A has at most 3 elements then MPOLSAT(A) is in P when width of P(A) is at most 2 and is NP-complete otherwise. We show also that if P � = NP then the class of unary algebras solvable in polynomial time is not closed under homomorphic images.

14. Linkable Dynkin diagrams and Quasi-isomorphisms for finite dimensional pointed Hopf algebras - Hopf Algebras,Daniel Didt
this paper in this relatively simple case again, so we can show how our method works. The notations are like in [BDR]

15. Computer algebra in modern functional languages. - Malaquias, José Romildo
Many computer algebra systems have already been proposed and implemented. Most of them are implemented in or even implement languages without the referential transparency property, making it difficult, if not impractical, to reason about algebra programs. This dissertation presents a computer algebra system implemented as a library in the Haskell programming language, a modern functional language with the desired referential transparency property. The author presents the foundations and basic algorithms for manipulation of algebraic expressions in a declarative context, compatible with Mathematics. He examines the adequacy of the constructs provided by the Haskell programming language for implementing such a library...

16. An Extended Algebra for Constraint Databases - Alberto Belussi; Elisa Bertino; Barbara Catania
Constraint relational databases use constraints to both model and query data. A constraint relation contains a finite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the specific conjunction of constraints, it may possibly represent an infinite set of relational tuples. For their characteristics, constraint databases are well suited to model multidimensional and structured data, like spatial and temporal data. The definition of an algebra for constraint relational databases is important in order to make constraint databases a practical technology. In this paper,...

17. Decomposition Of Algebras Over Finite Fields And Number Fields - Wayne Eberly
We consider the boolean complexity of the decomposition of semi-simple algebras over finite fields and number fields.

18. Composition Algebra -- from MathWorld - Weisstein, Eric W.
See: Real Normed Algebra

19. The Ziegler and Zariski spectra of some domestic string algebras - Kevin Burke; Mike Prest
It was a conjecture of the second author that the Cantor-Bendixson rank of the Ziegler spectrum of a nite-dimensional algebra is either less than or equal to 2 or is undened. Here we refute this conjecture by describing the Ziegler spectra of some domestic string algebras where arbitrary nite values greater than 2 are obtained. We give a complete description of the Ziegler and Gabriel-Zariski spectra of the simplest of these algebras. The conjecture has been independently refuted by Schroer [21] who, extending his work [20] on these algebras, computed their Krull-Gabriel dimension. 1 Indecomposable pure-injectives over domestic string algebras...

20. Projeto de interfaces para álgebra de mapas em geoprocessamento no ambiente SPRING - Ivan Soares de Lucena
Os Sistemas de Informação Geográfica (SIG)oferecem procedimentos de manipulação de mapas para que o usuário possa expressar modelos de análise espacial. Estes procedimentos, denominados Álgebra de Mapas, usualmente são expressos em linguagens, que permitem ordenar seqüências de transformações do dados geográficos para gerar novos mapas a partir dos mapas existentes. O Sistema de Processamento de Informações Georeferenciadas (SPRING), desenvolvido pelo Instituto Nacional de Pesquisas Espaciais (INPE), possui uma linguagem para Álgebra de Mapas denominada: Linguagem Espacial para Geoprocessamento Algébrico (LEGAL). Apesar do grande poder expressivo de uma linguagens como LEGAL, seu uso requer noções de fundamentos de programação, competência nem...

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