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Representation Theory of Artin Algebras
 Studies in Advanced Mathematics
, 1994
"... The representation theory of artin algebras, as we understand it today, is a relatively new area of mathematics, as most of the main developments have occurred ..."
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Cited by 644 (10 self)
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The representation theory of artin algebras, as we understand it today, is a relatively new area of mathematics, as most of the main developments have occurred
Comprehending Monads
 Mathematical Structures in Computer Science
, 1992
"... Category theorists invented monads in the 1960's to concisely express certain aspects of universal algebra. Functional programmers invented list comprehensions in the 1970's to concisely express certain programs involving lists. This paper shows how list comprehensions may be generalised t ..."
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Cited by 521 (18 self)
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Category theorists invented monads in the 1960's to concisely express certain aspects of universal algebra. Functional programmers invented list comprehensions in the 1970's to concisely express certain programs involving lists. This paper shows how list comprehensions may be generalised
The homogeneous coordinate ring of a toric variety
, 1992
"... This paper will introduce the homogeneous coordinate ring S of a toric variety X. The ring S is a polynomial ring with one variable for each onedimensional cone in the fan ∆ determining X, and S has a natural grading determined by the monoid of effective divisor classes in the Chow group An−1(X) of ..."
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Cited by 474 (7 self)
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) of X (where n = dim X). Using this graded ring, we will show that X behaves like projective space in many ways. The paper is organized into four sections as follows. In §1, we define the homogeneous coordinate ring S of X and compute its graded pieces in terms of global sections of certain coherent
Submodular functions, matroids and certain polyhedra
, 2003
"... The viewpoint of the subject of matroids, and related areas of lattice theory, has always been, in one way or another, abstraction of algebraic dependence or, equivalently, abstraction of the incidence relations in geometric representations of algebra. Often one of the main derived facts is that all ..."
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Cited by 355 (0 self)
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of linear programming. It turns out to be useful to regard “pure matroid theory”, which is only incidentally related to the aspects of algebra which it abstracts, as the study of certain classes of convex polyhedra. (1) A matroid M = (E,F) can be defined as a finite set E and a nonempty family F of so
Algebraic structures on parallel M2branes
 Nucl. Phys. B
"... In the course of closing supersymmetry on parallel M2 branes up to a gauge transformation, following the suggestion in hepth/0611108 of incorporating a gauge field which only has topological degrees of freedom, we are led to assume a certain algebraic structure for the low energy theory supposedly ..."
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Cited by 383 (2 self)
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In the course of closing supersymmetry on parallel M2 branes up to a gauge transformation, following the suggestion in hepth/0611108 of incorporating a gauge field which only has topological degrees of freedom, we are led to assume a certain algebraic structure for the low energy theory supposedly
Data Exchange: Semantics and Query Answering
 In ICDT
, 2003
"... Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema that reflects the source data as accurately as possible. In this paper, we address foundational and algorithmic issues related to the semantics of data exchange and to query answe ..."
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Cited by 425 (41 self)
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answering in the context of data exchange. These issues arise because, given a source instance, there may be many target instances that satisfy the constraints of the data exchange problem. We give an algebraic specification that selects, among all solutions to the data exchange problem, a special class
Universal coalgebra: a theory of systems
, 2000
"... In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certa ..."
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Cited by 407 (42 self)
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for certain types of automata and more generally, for (transition and dynamical) systems. An important property of initial algebras is that they satisfy the familiar principle of induction. Such a principle was missing for coalgebras until the work of Aczel (NonWellFounded sets, CSLI Leethre Notes, Vol. 14
DIMENSIONS OF TRIANGULATED CATEGORIES VIA KOSZUL OBJECTS
"... Abstract. Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for the representation dimensions of certain Artin alge ..."
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Cited by 20 (10 self)
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Abstract. Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for the representation dimensions of certain Artin
Extending the Database Relational Model to Capture More Meaning
 ACM Transactions on Database Systems
, 1979
"... During the last three or four years several investigators have been exploring “semantic models ” for formatted databases. The intent is to capture (in a more or less formal way) more of the meaning of the data so that database design can become more systematic and the database system itself can beha ..."
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Cited by 337 (2 self)
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to support certain atomic and molecular semantics. These extensions represent a synthesis of many ideas from the published work in semantic modeling plus the introduction of new rules for insertion, update, and deletion, as well as new algebraic operators.
Results 1  10
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334,443