On Sheaf Representation of a Biregular Near-Ring

1977 ◽  
Vol 20 (4) ◽  
pp. 495-500 ◽  
Author(s):  
George Szeto
Keyword(s):  
Boolean Space ◽  
Sheaf Representation

AbstractIt is shown that R is a biregular near-ring if and only if it is isomorphic with the near-ring of sections of a sheaf of reduced near-rings over a Boolean space. Also, some ideal properties of a biregular near-ring are proved. These are considered as generalizations of some works of R. Pierce on biregular rings.

scholarly journals The Boolean space of higher level orderings

2007 ◽  
Vol 196 (2) ◽  
pp. 101-117 ◽  
Author(s):  
Katarzyna Osiak
Keyword(s):  
Boolean Space

A generic sheaf representation for rings

1991 ◽  
pp. 30-42 ◽  
Author(s):  
Francis Borceux ◽  
Gilberte Van den bossche
Keyword(s):  
Sheaf Representation

The Lattice of Subalgebras of a Boolean Algebra

1962 ◽  
Vol 14 ◽  
pp. 451-460 ◽  
Author(s):  
David Sachs
Keyword(s):  
Boolean Algebra ◽  
Lattice Theory ◽  
Closure Operator ◽  
Vector Spaces ◽  
Finite Partition ◽  
Partition Lattice ◽  
Topological Vector Spaces ◽  
Boolean Space ◽  
Lattice Of Subalgebras

It is well known (1, p. 162) that the lattice of subalgebras of a finite Boolean algebra is dually isomorphic to a finite partition lattice. In this paper we study the lattice of subalgebras of an arbitrary Boolean algebra. One of our main results is that the lattice of subalgebras characterizes the Boolean algebra. In order to prove this result we introduce some notions which enable us to give a characterization and representation of the lattices of subalgebras of a Boolean algebra in terms of a closure operator on the lattice of partitions of the Boolean space associated with the Boolean algebra. Our theory then has some analogy to that of the lattice theory of topological vector spaces. Of some interest is the problem of classification of Boolean algebras in terms of the properties of their lattice of subalgebras, and we obtain some results in this direction.

Sheaf representation and Chinese remainder theorems

1992 ◽  
Vol 29 (2) ◽  
pp. 232-272 ◽  
Author(s):  
Diego J. Vaggione
Keyword(s):  
Sheaf Representation

scholarly journals A note on commutative Baer rings III

1973 ◽  
Vol 15 (1) ◽  
pp. 15-21 ◽  
Author(s):  
T. P. Speed
Keyword(s):  
Semiprime Ring ◽  
Boolean Space ◽  
Baer Ring ◽  
Baer Rings

If R is a commutative semiprime ring with identity Kist [4], [5] has shown that R can be embedded into a commutative Baer ring B(R), and has given some properties of this embedding. More recently Mewborn [7] has given a construction which embeds R into a commutative Baer ring with the stronger property that every annihilator is generated by an idempotent. Both of these constructions involve a representation of R as a ring of global sections of a sheaf over a Boolean space.

A Sheaf Representation of Principally Quasi-Baer ∗-Rings

2018 ◽  
Vol 22 (1) ◽  
pp. 79-97
Author(s):  
Anil Khairnar ◽  
B. N. Waphare
Keyword(s):  
Sheaf Representation ◽  
Baer Rings

scholarly journals An ordered sheaf representation of subresiduated lattices

1980 ◽  
Vol 22 (1) ◽  
pp. 125-132 ◽  
Author(s):  
William H. Cornish
Keyword(s):  
Priestley Space ◽  
Sheaf Representation

Kennison's concept of an ordered sheaf is used to show that any member of the variety of subresiduated lattices is canonically isomorphic to the algebra of all ordered sections in a certain ordered sheaf, whose base is the Priestley space of the residuating sublattice.

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