Semigroups, Algebras and Operator Theory: Kochi, India, February 2014

217 Pages·2015·2.725 MB·English

by  P G Romeo, John. C Meakin, A R Rajan (eds.)

Springer Proceedings in Mathematics & Statistics
P.G. Romeo
John C. Meakin
A.R. Rajan Editors
Semigroups,
Algebras and
Operator
Theory
Kochi, India, February 2014
Springer Proceedings in Mathematics & Statistics
Volume 142
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P.G. Romeo John C. Meakin
(cid:129)
A.R. Rajan
Editors
Semigroups, Algebras
and Operator Theory
Kochi, India, February 2014
123
Editors
P.G. Romeo A.R. Rajan
Department ofMathematics Department ofMathematics
CochinUniversity ofScience and University of Kerala
Technology(CUSAT) Thiruvananthapuram, Kerala
Kochi, Kerala India
India
JohnC. Meakin
Department ofMathematics
University of Nebraska
Lincoln, NE
USA
ISSN 2194-1009 ISSN 2194-1017 (electronic)
SpringerProceedings in Mathematics& Statistics
ISBN978-81-322-2487-7 ISBN978-81-322-2488-4 (eBook)
DOI 10.1007/978-81-322-2488-4
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Preface
The International Conference on Semigroups, Algebras and Operator Theory
(ICSAOT-2014) focused on the recent advances in semigroup theory and operator
theory. The scientific programs emphasized on the research related to the structure
theoryofsemigroup,semigroupapproachtoVonNeumannregularityandoperator
algebras. The conference was hosted by the Department of Mathematics, Cochin
University of Science and Technology (CUSAT), Kochi, Kerala, India during
26–28 February 2014.
Leading researchers from 11 different countries working in these areas were
invited to participate. A total of 63 delegates including Ph.D. students from eight
countries participated. The following plenary lectures were given:
1. John C. Meakin, University of Nebraska, USA—Amalgams of Inverse
Semigroups of C(cid:1)—Algebras.
2. Laszlo Marki, Budapest, Hungary—Commutative Order in Semigroups.
3. M.V. Volkov, University of Ekaterinburg, Russia—The Finite Basis Problem
for Kauffman Monoids.
4. Alessandra Cherubini, Milano, Italy—Word Problem in Amalgams of Inverse
Semigroups.
5. K.S.S. Nambooripad, Kerala, India—von Neumann Algebras and Semigroups.
6. M.K. Sen, Kolkata, India—Left Clifford Semigroups.
7. Pascal Weil, LaBRI-CNBS, Talence Cedex, France—Logic, Language and
Semigroups: from the lattice of band varites to the quantifier alteration hier-
archy within the 2-variable fragment offirst order logic.
8. Jorge Almeida, Alegre, Portugal—Irreducibility of Psedovarieties of
Semigroup.
9. B.V. Limaye, Mumbai, India—Operator Approximations.
10. S.H. Kulkarni, Chennai, India—The Null Space Theorem.
11. M. Thamban Nair, Chennai, India—Role of Hilbert Scales in Regularization
Theory.
The daily program consisted of lectures, paper presentations and discussions
held in an open and encouraging atmosphere.
v
vi Preface
Inadditiontotheabovespeakerstherewereinvitedtalksandpaperpresentations.
Wearegreatfultoallparticipantsfortheirvaluablecontributionsandformakingthe
ICSAOT-2014a successfull event. Moreover, we would like tothank theNational
BoardforHigherMathematics,DAE,Mumbai;CSIR,NewDelhi;SERB-DST,New
Delhi; KSCSTE, Thiruvananthapuram for providing us with financial support. We
arealsothankfultotheCochinUniversityofScienceandTechnologyforadditional
support and practical assistance related to the preparation and organization of the
conference.Wethankallourrefereesfortheirsincerecooperation,whichenabledthe
successfulcompletionoftherefereeingprocesses.
P.G. Romeo
John C. Meakin
A.R. Rajan
Contents
Decidability Versus Undecidability of the Word Problem
in Amalgams of Inverse Semigroups. . . . . . . . . . . . . . . . . . . . . . . . . . 1
Alessandra Cherubini and Emanuele Rodaro
A Nonfinitely Based Semigroup of Triangular Matrices. . . . . . . . . . . . 27
M.V. Volkov
Regular Elements in von Neumann Algebras . . . . . . . . . . . . . . . . . . . 39
K.S.S. Nambooripad
LeftRight Clifford Semigroups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
M.K. Sen
Certain Categories Derived from Normal Categories. . . . . . . . . . . . . . 57
A.R. Rajan
Semigroup Ideals and Permuting 3-Derivations in Prime
Near Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Asma Ali, Clauss Haetinger, Phool Miyan and Farhat Ali
Biordered Sets and Regular Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
P.G. Romeo
Topological Rees Matrix Semigroups . . . . . . . . . . . . . . . . . . . . . . . . . 89
E. Krishnan and V. Sherly
Prime Fuzzy Ideals, Completely Prime Fuzzy Ideals
of Po-C-Semigroups Based on Fuzzy Points . . . . . . . . . . . . . . . . . . . . 105
Pavel Pal, Sujit Kumar Sardar and Rajlaxmi Mukherjee Pal
vii
viii Contents
Radicals and Ideals of Affine Near-Semirings
Over Brandt Semigroups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Jitender Kumar and K.V. Krishna
Operator Approximation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Balmohan V. Limaye
The Nullity Theorem, Its Generalization and Applications. . . . . . . . . . 149
S.H. Kulkarni
Role of Hilbert Scales in Regularization Theory . . . . . . . . . . . . . . . . . 159
M.T. Nair
On Three-Space Problems for Certain Classes of C*-algebras . . . . . . . 177
A.K. Vijayarajan
Spectral Approximation of Bounded Self-Adjoint
Operators—A Short Survey. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
K. Kumar
On k-Minimal and k-Maximal Operator Space Structures. . . . . . . . . . 205
P. Vinod Kumar and M.S. Balasubramani
Editors and Contributors
About the Editors
P.G.Romeo isprofessorandheadoftheDepartmentofMathematicsattheCochin
University of Science and Technology (CUSAT), Kochi, Kerala, India. His major
research interests include semigroups theory, representation theory, universal
algebrasandcategorytheory.HeearnedhisPh.D.fromtheUniversityofKeralain
1993undertheguidanceofProf.K.S.S.Nambooripad.Duringhisillustriouscareer
asresearcherandprofessorforovertwodecades,Prof.Romeotaughtawidevariety
of courses both at undergraduate and graduate levels. He also guides students for
doctoral research. He has published research articles with various peer-reviewed
international mathematics journals as well as given invited talks at various inter-
national and national conferences.
JohnC.Meakin istheMiltonMohrProfessorofMathematicsattheUniversityof
Nebraska-Lincoln, USA.Heservedasthechair oftheDepartment ofMathematics
at Nebraska during 2003–2011. His primary research interests include modern
algebra and theoretical computer science, with particular focus on the algebraic
theory of semigroups and geometric group theory. He teaches a wide variety of
courses ranging from freshman-level calculus to advanced graduate courses in
algebraandtopology.ProfessorMeakinhaspublishedextensivelyinpeer-reviewed
international mathematics journals and has served for 20 years as managing editor
ofInternationalJournalofAlgebraandComputation.Electedin2014asaFellow
oftheAmericanMathematicalSociety,Prof.Meakinhasgivenaround200invited
lectures at conferences and universities around the world and has held extended
visiting positions in Australia, Belgium, France, India, Israel, Italy, Spain and the
USA.
A.R.Rajan isanemeritusprofessorattheDepartmentofMathematics,University
of Kerala, India. He earned his Ph.D. and M.A. (Russian language) from Kerala
University. He also held positions such as member of the senate and syndicate
of the University of Kerala and chairman of the board of studies in mathematics.
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