1. |
Four dimensional regular algebras with point scheme, anonsingular quadric in P3 |
|
Communications in Algebra,
Volume 28,
Issue 5,
2000,
Page 2211-2242
Michaela Vancliff,
Kristel Van Rompay,
Preview
|
PDF (1547KB)
|
|
摘要:
In [22], a class of four-dimensional, quadratic, Artin-Schelter regular algebras was introduced, whose point scheme is the graph of an automorphism of a nonsingular quadric in P3. These algebras are the first examples of quadratic Artin-Schelter regular algebras whose defining relations are not determined by the point scheme and, hence, not determined by the algebraic data obtained from the point modules. In this paper, we study these algebras via their line modules. In particular, the set of lines in P3that correspond to left line modules is not the set of lines in P3that correspond to right line modules. Our analysis focuses on a distinguished memberRλof this class of algebras, whereRλis a twist by a twisting system of the other algebras. We prove thatRλis a finite module over its center and that its central Proj is a smooth quadric inP4.
ISSN:0092-7872
DOI:10.1080/00927870008826955
出版商:Gordon and Breach Science Publishers Ltd.
年代:2000
数据来源: Taylor
|
2. |
Lie-admissible algebras and generalized witt algebras* |
|
Communications in Algebra,
Volume 28,
Issue 5,
2000,
Page 2243-2252
Yuting Jia,
Preview
|
PDF (259KB)
|
|
ISSN:0092-7872
DOI:10.1080/00927870008826956
出版商:Gordon and Breach Science Publishers Ltd.
年代:2000
数据来源: Taylor
|
3. |
Solutions of yang-baxter equation in an endomorphism semigroup and quasi-(co)braided almost bialgebras* |
|
Communications in Algebra,
Volume 28,
Issue 5,
2000,
Page 2253-2270
Fang Li,
Preview
|
PDF (577KB)
|
|
摘要:
The aim of this paper is to study the solutions of the Yang-Baxter equation in the endomorphism semigroup of the tensor product of a vector space. As preparation, we introduce the concepts of quasi-braided almost bialgebra (see also [10]) and quasi-cobraided almost bialgebra, and discuss some of their properties. In particular, it is shown that the quasi R-matrixRof every quasi-braided almost weak Hopf algebra is regular under von Neumann's meaning. The solutions of the Yang-Baxter equation in the endomorphism semigroups are constructed respectively from every quasi-braided almost bialgebra and every quasi-cobraided almost bialgebra. As examples, we explain how to build solutions of the Yang-Baxter equation from some weak Hopf algebras and all Clifford monoids. Finally, the FRT construction is given so as to build every solution of the Yang-Baxter equation from a quasi-cobraided bialgebra.
ISSN:0092-7872
DOI:10.1080/00927870008826957
出版商:Gordon and Breach Science Publishers Ltd.
年代:2000
数据来源: Taylor
|
4. |
The number of homomorphisms from a finite abelian group to a symmetric group |
|
Communications in Algebra,
Volume 28,
Issue 5,
2000,
Page 2271-2290
Hidenori Katsurada,
Yugen Takegahara,
Tomoyuki Yoshida,
Preview
|
PDF (444KB)
|
|
ISSN:0092-7872
DOI:10.1080/00927870008826958
出版商:Gordon and Breach Science Publishers Ltd.
年代:2000
数据来源: Taylor
|
5. |
Some remarks on dense submodules of multiplication modules |
|
Communications in Algebra,
Volume 28,
Issue 5,
2000,
Page 2291-2296
Yücel Tiras,
Abdullah Harmanci,
P.F. Smith,
Preview
|
PDF (233KB)
|
|
ISSN:0092-7872
DOI:10.1080/00927870008826959
出版商:Gordon and Breach Science Publishers Ltd.
年代:2000
数据来源: Taylor
|
6. |
Two dimensional coordinate polynomials and dominant maps |
|
Communications in Algebra,
Volume 28,
Issue 5,
2000,
Page 2297-2301
L. Andrew Campbell,
Jie-Tai Yu,
Preview
|
PDF (188KB)
|
|
摘要:
A polynomial in n variables is called a coordinate polynomial if it is a component of a polynomial automorphism ofn-space. Forn=2 and a ground field of characteristic zero, we show that a polynomial is a coordinate polynomial if its composition with a dominant endomorphism of 2-space is a coordinate polynomial.
ISSN:0092-7872
DOI:10.1080/00927870008826960
出版商:Gordon and Breach Science Publishers Ltd.
年代:2000
数据来源: Taylor
|
7. |
Quantum doubles in monoidal categories |
|
Communications in Algebra,
Volume 28,
Issue 5,
2000,
Page 2303-2328
Hui-Xiang Chen,
Preview
|
PDF (588KB)
|
|
摘要:
LetHbe a Hopf algebra in a rigid symmetric monoidal categoryCthen the evaluation map τis a convolution-invertible skew pairing. In the previous paper, we constructed a Hopf algebraD(H)=H⋈rH*copinC. In this paper, we first show thatD(H) is a quasitriangular Hopf algebra inC. Next, letHbe an ordinary triangular finite-dimensional Hopf algebra. Then one can form quasitriangular Hopf algebrasB(H,H)andB(H,D(H))(in a rigid braided monoidal category) by Majid’s method associated to the ordinary Hopf algebra mapsH→HandiHH→D(H), whereD(H)is the Drin-fePd quantum double. We show thatD(B(H,H))andB(H,D(H))are isomorphic Hopf algebras in the braided monoidal category.
ISSN:0092-7872
DOI:10.1080/00927870008826961
出版商:Gordon and Breach Science Publishers Ltd.
年代:2000
数据来源: Taylor
|
8. |
A topological characterization of the goldman prime spectrum of a commutative ring |
|
Communications in Algebra,
Volume 28,
Issue 5,
2000,
Page 2329-2337
Othman Echi,
Preview
|
PDF (217KB)
|
|
摘要:
A prime idealpof a commutative ringRis said to be a Goldman ideal (or aG-ideal) if there exists a maximal idealMof the polynomial ringR[X] such thatp=M∩R. A topological space is said to be goldspectral if it is homeomorphic to the space Gold(R) ofG-ideals ofR(Gold(R) is considered as a subspace of the prime spectrum Spec(R) equipped with the Zariski topology). We give here a topological characterization of goldspectral spaces.
ISSN:0092-7872
DOI:10.1080/00927870008826962
出版商:Gordon and Breach Science Publishers Ltd.
年代:2000
数据来源: Taylor
|
9. |
Integral ring extensions and lo-pairs |
|
Communications in Algebra,
Volume 28,
Issue 5,
2000,
Page 2339-2341
R. Debremaeker,
V. Van Lierde,
Preview
|
PDF (115KB)
|
|
摘要:
We give an example of an LO-pair (R,T) with dimR=dimT=n, so that all maximal ideals ofRhave the same heightn, but withTnot integral overR. This answers an open question of DavidE. Dobbs.
ISSN:0092-7872
DOI:10.1080/00927870008826963
出版商:Gordon and Breach Science Publishers Ltd.
年代:2000
数据来源: Taylor
|
10. |
Remarks on pseudo-valuation rings |
|
Communications in Algebra,
Volume 28,
Issue 5,
2000,
Page 2343-2358
Ayman Badawi,
Preview
|
PDF (373KB)
|
|
摘要:
A prime ideal P of a ring A is said to be a strongly prime ideal if aP and bA are comparable for all a,b ϵ A. We shall say that a ring A is a pseudo-valuation ring (PVR) if each prime ideal of A is a strongly prime ideal. We show that if A is a PVR with maximal ideal M, then every overring of A is a PVR if and only if M is a maximal ideal of every overring of M that does not contain the reciprocal’of any element of M.We show that if R is an atomic domain and a PVD, then dim(R) ≤ 1. We show that if R is a PVD and a prime ideal of R is finitely generated, then every overring of R is a PVD. We give a characterization of an atomic PVD in terms of the concept of half-factorial domain.
ISSN:0092-7872
DOI:10.1080/00927870008826964
出版商:Gordon and Breach Science Publishers Ltd.
年代:2000
数据来源: Taylor
|