scholarly journals On Bilinear Forms from the Point of View of Generalized Effect Algebras

2013 ◽  
Vol 43 (9) ◽  
pp. 1136-1152 ◽  
Author(s):  
Anatolij Dvurečenskij ◽  
Jiří Janda
Keyword(s):  
Point Of View ◽  
Bilinear Forms ◽  
Effect Algebras ◽  
Generalized Effect Algebras

Signatures and Semi Signatures of Abstract Witt Rings and Witt Rings of Semilocal Rings

1978 ◽  
Vol 30 (4) ◽  
pp. 872-895 ◽  
Author(s):  
Jerrold L. Kleinstein ◽  
Alex Rosenberg
Keyword(s):  
Residue Class ◽  
Point Of View ◽  
Prime Ideals ◽  
Bilinear Forms ◽  
Semilocal Ring ◽  
Witt Ring ◽  
Witt Rings ◽  
Full Knowledge ◽  
Carry Over

This paper originated in an attempt to carry over the results of [3] from the case of a field of characteristic different from two to that of semilocal rings. To carry this out, we reverse the point of view of [3] and do assume a full knowledge of the theory of Witt rings of classes of nondegenerate symmetric bilinear forms over semilocal rings as given, for example, in [10; 11]. It turns out that the rings WT of [3] are just the residue class rings of W(C), the Witt ring of a semilocal ring C, modulo certain intersections of prime ideals.

scholarly journals Weakly ordered partial commutative group of self-adjoint linear operators densely defined on Hilbert space

2011 ◽  
Vol 50 (1) ◽  
pp. 63-78
Author(s):  
Jiří Janda
Keyword(s):  
Hilbert Space ◽  
Algebraic Structure ◽  
Complex Hilbert Space ◽  
Commutative Group ◽  
Pt Symmetry ◽  
Linear Operators ◽  
Effect Algebras ◽  
Infinite Dimensional ◽  
Densely Defined ◽  
Generalized Effect Algebras

ABSTRACT We continue in a direction of describing an algebraic structure of linear operators on infinite-dimensional complex Hilbert space ℋ. In [Paseka, J.- -Janda, J.: More on PT-symmetry in (generalized) effect algebras and partial groups, Acta Polytech. 51 (2011), 65-72] there is introduced the notion of a weakly ordered partial commutative group and showed that linear operators on H with restricted addition possess this structure. In our work, we are investigating the set of self-adjoint linear operators on H showing that with more restricted addition it also has the structure of a weakly ordered partial commutative group.

Topological Properties of Operator Generalized Effect Algebras

2012 ◽  
Vol 69 (3) ◽  
pp. 311-320 ◽  
Author(s):  
S. Pulmannová ◽  
Z. Riečanová ◽  
M. Zajac
Keyword(s):  
Effect Algebras ◽  
Topological Properties ◽  
Generalized Effect Algebras

Riesz ideals in generalized effect algebras and in their unitizations

2007 ◽  
Vol 57 (4) ◽  
pp. 393-417 ◽  
Author(s):  
S. Pulmannová ◽  
E. Vinceková
Keyword(s):  
Effect Algebras ◽  
Generalized Effect Algebras

Blocks in Pairwise Summable Generalized Effect Algebras

2014 ◽  
Vol 73 (2) ◽  
pp. 213-223
Author(s):  
Zdenka Riečanová ◽  
Jiří Janda ◽  
Wu Junde
Keyword(s):  
Effect Algebras ◽  
Generalized Effect Algebras
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