NOTE: This item is not available outside the Texas A&M University network. Texas A&M affiliated users who are off campus can access the item through NetID and password authentication or by using TAMU VPN. Non-affiliated individuals should request a copy through their local library's interlibrary loan service.
On the endomorphism monoids of Boolean algebras and distributive lattices
dc.contributor.advisor | Rose, Norman C. | |
dc.creator | Natarajan, Ponnammal | |
dc.date.accessioned | 2020-01-08T17:48:40Z | |
dc.date.available | 2020-01-08T17:48:40Z | |
dc.date.created | 1974 | |
dc.date.issued | 1967 | |
dc.identifier.uri | https://hdl.handle.net/1969.1/DISSERTATIONS-172535 | |
dc.description.abstract | This work is concerned with some questions which arise in the study of endomorphism monoids of Boolean algebras and finite distributive lattices. It is a well known fact that the automorphism group does not characterize a Boolean algebra. New examples to verify the above fact are obtained by considering the finite confinite Boolean algebra on an infinite set X, and its generalizations, we obtain new examples of non-isomorphic Boolean algebras in which the automorphism groups are isomomorphic. It is shown that there exist an infinite number of non-isomorphic Boolean algebras with automorphism groups anti-isomorphic to S(X), the symmetric group of transformations on a set X. C. J. Maxson has shown that for the Boolean algebra 2 [superscript X], the monoid of complete endomorphisms is anti-isomorphic to T(X), the monoid of transformations on X. This motivates the problem of finding Boolean algebras for which every endomorphism is complete. It is shown here that if U is a complete (atomic) Boolean algebra then every endomorphism of U is complete if and only if U is finite. | en |
dc.format.extent | 77 leaves | en |
dc.format.medium | electronic | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.rights | This thesis was part of a retrospective digitization project authorized by the Texas A&M University Libraries. Copyright remains vested with the author(s). It is the user's responsibility to secure permission from the copyright holder(s) for re-use of the work beyond the provision of Fair Use. | en |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject.classification | 1974 Dissertation N274 | |
dc.title | On the endomorphism monoids of Boolean algebras and distributive lattices | en |
dc.type | Thesis | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Texas A&M University | en |
thesis.degree.name | Doctor of Philosophy | en |
thesis.degree.level | Doctoral | en |
dc.contributor.committeeMember | Hancock, C. Kinney | |
dc.contributor.committeeMember | Jones, Jerry L. | |
dc.contributor.committeeMember | Lyman, Carl M. | |
dc.contributor.committeeMember | Prescott, J. M. | |
dc.type.genre | dissertations | en |
dc.type.material | text | en |
dc.format.digitalOrigin | reformatted digital | en |
dc.publisher.digital | Texas A&M University. Libraries |
Files in this item
This item appears in the following Collection(s)
-
Digitized Theses and Dissertations (1922–2004)
Texas A&M University Theses and Dissertations (1922–2004)
Request Open Access
This item and its contents are restricted. If this is your thesis or dissertation, you can make it open-access. This will allow all visitors to view the contents of the thesis.