Author
Chia Hsin Liu
Other affiliations: National Cheng Kung University, National Sun Yat-sen University, Beijing Normal University ...read more
Bio: Chia Hsin Liu is an academic researcher from National Taiwan Normal University. The author has contributed to research in topics: Group ring & Multiplicative function. The author has an hindex of 6, co-authored 16 publications receiving 185 citations. Previous affiliations of Chia Hsin Liu include National Cheng Kung University & National Sun Yat-sen University.
Papers
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01 Dec 1999
TL;DR: In this article, the original Hartley conjecture was extended to handle fields of all sizes, and the original proof was verified in case K is an infinite field and U(K[G]) satisfies a polynomial identity.
Abstract: Let K[G] be the group algebra of a group G over a field K, and let U(K[G]) be its group of units. A conjecture by Brian Hartley asserts that if G is a torsion group and U(K[G]) satisfies a group identity, then K[G] satisfies a polynomial identity. This was verified earlier in case K is an infinite field. Here we modify the original proof so that it handles fields of all sizes.
60 citations
01 Jan 1999
43 citations
TL;DR: In this paper, a necessary condition for twisted group algebras to satisfy a generalized polynomial identity is given. But this condition is not satisfied for all twisted groups.
Abstract: We study locally finite algebras and twisted group algebras with units satisfying a group identity. As a preliminary result, we obtain a necessary condition for twisted group algebras to satisfy a generalized polynomial identity.
22 citations
TL;DR: In this paper, it was shown that any GI-ring is Dedekind finite (von Neumann finite) and Nilpotent elements of a semiprimitive GI ring have bounded index.
17 citations
Illinois Institute of Technology1, Valparaiso University2, University of Tarapacá3, Florida State University4, American University in Cairo5, Universidade Estadual de Londrina6, University of Bordeaux7, Weizmann Institute of Science8, Pontifical Catholic University of Peru9, National Autonomous University of Mexico10, Khon Kaen University11, William Woods University12, Marmara University13, Kent State University14, University of Tsukuba15, University of Pretoria16, National Pedagogic University (Mexico)17, Beijing Normal University18, Laurentian University19, Stockholm University20, University of Seville21, University of Cape Town22, University of Akron23, Zhejiang Normal University24, University of Ioannina25, Leibniz University of Hanover26, National Pingtung University27, University of Helsinki28, University of Hong Kong29, Arizona State University30, National Changhua University of Education31, National Taiwan Normal University32, Griffith University33, University of Vienna34, Instituto Politécnico Nacional35, Zhejiang International Studies University36, Mahidol University37, University of Johannesburg38, Centre national de la recherche scientifique39, Georgia State University40, Fiji National University41, University of British Columbia42, University of Bristol43
TL;DR: Lederman et al. as discussed by the authors conducted an international collaborative investigation of beginning seventh grade students' understandings of scientific inquiry: Establishing a baseline for science education reform documents around the world.
Abstract: Understandings of the nature of scientific inquiry (NOSI), as opposed to engaging students in inquiry learning experiences, are included in science education reform documents around the world. However, little is known about what students have learned about NOSI during their pre-college school years. The purpose of this large-scale follow-up international project (i.e. 32 countries and regions, spanning six continents and including 3917 students for the high school sample) was to collect data on what exiting high school students have learned about NOSI. Additionally, the study investigated changes in 12th grade students’ NOSI understandings compared to seventh grade (i.e. 20 countries and regions) students’ understandings from a prior investigation [Lederman et al. (2019). An international collaborative investigation of beginning seventh grade students’ understandings of scientific inquiry: Establishing a baseline. Journal of Research in Science Teaching, 56(4), 486–515. https://doi.org/10.1002/tea.21512]. This study documents and discusses graduating high school students’ understandings and compares their understandings to seventh grade students’ understandings of the same aspects of scientific inquiry for each country. It is important to note that collecting data from each of the 130+ countries globally was not feasible. Similarly, it was not possible to collect data from every region of each country. A concerted effort was made, however, to provide a relatively representative picture of each country and the world.
9 citations
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TL;DR: In this paper, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
Abstract: This text, drawn from the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-term course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semi-simple rings, Jacobson's theory of the radical representation theory of groups and algebras, prime and semi-prime rings, primitive and semi-primitive rings, division rings, ordered rings, local and semi-local rings, and perfect and semi-perfect rings. By aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation, the author has produced a text which is suitable not only for use in a graduate course, but also for self-study by other interested graduate students. Numerous exercises are also included. This graduate textbook on rings, fields and algebras is intended for graduate students in mathematics.
1,479 citations
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TL;DR: In this window, all groups are assumed finite as discussed by the authors, and a number of results of an elementary nature that we sometimes take for granted is easily available in textbooks such as [H], [R] and [A]).
Abstract: In this window, all groups are assumed finite. Here we collect a number of results that play a significant role in the book (further material of an elementary nature that we sometimes take for granted is easily available in textbooks such as [H], [R] and [A]).
310 citations
01 Jan 1999
43 citations
Journal Article•
TL;DR: A short survey article as mentioned in this paper reviews the current state of understanding of the structure of noetherian Hopf algebras, focusing on homological properties and a number of open problems.
Abstract: This short survey article reviews our current state of understanding of the structure of noetherian Hopf algebras. The focus is on homological properties. A number of open problemsare lis ted.
40 citations