On Representability of *-Regular and Regular Involutive Rings in Endomorphism Rings of Vector Spaces
By (author) Niklas Niemann
(Paperback) (Published)
(April 2007)
ISBN: 9783832515638
5.71 x 8.27 inches
Price: $61.00
Out of stock
The origins of von Neumann-regular rings and *-regular rings are the works of John von Neumann and F. J. Murray during the 30ies of the last century. They constitute a connection of the areas of operator theory, ring theory and lattice theory. Starting from this historical origin, one can speculate that von Neumann was inspired by both operator theory and lattice theory to introduce the notion of a *-regular ring: On the one hand, the requirement of positivity of the involution can be seen as the appropriate generalisation of the involution of operator algebras. On the other hand, *-regular rings give rise to a strong class of lattices which are closely connected to operator algebras. This thesis shows that this speculation mighthave some substance, that is, the concept of a *-regular ring indeed gives an adequate axiomatic framework for regular rings of operators, if one is prepared to deal with vector spaces over general involutive skew fields, equipped with a scalar product. The main results of this thesis are that every *-regular ring is representable in this sense, and that every variety of *-regular rings is generated by its simple Artinian members. Furthermore, the thesis deals with the larger class of regular involutive rings and questions of their representability. In the context of rings without involution, Jacobson proved thatrepresentability as subrings of endomorphism rings of vector spaces is captured by primitivity. Dealing with involutive rings, onecan introduce the notion of *-primitivity and representations in terms of bi-vector spaces, as done by Rowen and Wiegandt. Alternatively, one can examine primitive rings endowed with an involution, with the aim to construct an appropriate non-degenerated form on the vector space to capture the involution. In this context, the thesis presents a continuation of previous research of Herrmann, Micol and Niemann. A complete characterisation of representability of regular involutive rings is given.
- By (author) Niklas Niemann
Similar Books
![Book cover: Transitive Media [Philosophy]](https://isd.stisonbooks.com/images/books/native/9781804132340.jpg?asset_id=66970)
Care in an Era of New Technologies and Artificial Intelligence
Relationships in a Connected World
Volume 14
Buchblogs zwischen Passion und Profession
Zur Diskursivierung digitaler literaturbezogener Anschlusskommunikation als Arbeit
Volume 5
Proceedings of the 7th Symposium of the Hellenic Society for Archaeometry
Archaeology Archaeometry: 30 Years Later
Die Einfuhrung ins richtige Handeln in der Arithmetik (Madhal ar-rasad ila ‘ilm al-‘adad) von al-Qalasadi (st. 1486)
Bearbeitung und Einordnung in die magribinische Mathematikgeschichte
Volume 19
I disegni e i discorsi di Giovanni Antonio Nigrone vol. I
fontanaro e ingegniero de acqua (1585-1609 ca.)
Volume 481
I disegni e i discorsi di Giovanni Antonio Nigrone vol. II
Fontanaro e ingegniero de acqua (1585-1609 ca.)
Volume 497
Performance Management in Humanitarian Logistics
Development of a Process-driven and IT-supported Performance Measurement System
Volume 66
Supporting Operational and Real-time Planning Tasks of Road Freight Transport with Machine Learning
Guiding the Implementation of Machine Learning Algorithms
Volume 69
