摘要:

A prime ideal P of a commutative ring R with identity is called strongly prime if aP and bR are comparable for every a, b in R. If every prime ideal of R is strongly prime, then R is called a pseudo-valuation ring. It is well-known that a (valuation) chained overring of a Prufer domain R is of the form RPfor some prime ideal P of R.In this paper, we show that this statement is valid for a certain class of chained overrings of a pseudo-valuation ring.

ISSN:0092-7872    

DOI:10.1080/00927870008826965

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

In this article we establish the conjecture of Huah Chu [8] on modular rational invariants of finite orthogonal groups over finite fields of characteristic two.

ISSN:0092-7872    

DOI:10.1080/00927870008826966

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826967

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetTbe a Gorenstein sequence of a graded artinian Gorenstein ringk[x0,x1,x2]/IWe develop a dimension formula for PGor(T)in terms of the alignment character. Based on our formula, we find a very large component ofVs(t,t,2) whens=rt-1+1andtis large enough. This answers Diesel’s conjecture negatively. Further we show thatVs(t,t,2) is irreducible of dimension 3s-1 fors≤t+1,t≥ 2 and dimVs(t,t,2)= 3s-1 for smalls. Finally an algorithm to calculate dimVs(t,t,2) is constructed, and we find the values of dimVs(t,t,2) fort≤ 16.

ISSN:0092-7872    

DOI:10.1080/00927870008826968

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We determine the nilpotent right alternative rings of prime power oirderpnn≥ 4, which are not left alternative. Those which are strongly right alternative become Bol loops under the circle operation. The smallest Bol circle loop has order 16. There are six such loops, all of which appear to be new.

ISSN:0092-7872    

DOI:10.1080/00927870008826969

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetDbe an integral domain with quotient fieldK, let (F(D) (f(D)) be the set of nonzero (finitely generated) fractional ideals ofD, and let ★ be a star-operation onF(D).ForA ∈ F(D) andthere existsJ∈f(D)such thatJ★=D, andxJ⊆A}.ThenA★w= {x ∈K| existsJ ∈ f(D) such thatJ★=D, and xJ⊆A}. Thenand ★ware star-operations onF(D)that satisfy. Moreover,is the greatest (finite character) star-operation Δ ≤ ★ with (A∩B)Δ=AΔ∩BΔ.We also show that ★w-Max(D)= ★s-Max(D) andA★w=∩{AP|P∈★s-Max(D)}.LetL★w(D) = {A|Ais an integral ★w-ideal}∪{0}. ThenL★w(D) forms anr-lattice. IfDsatisfiesACCon integral ★w-ideals,L*w(D) is a Noether lattice and hence primary decomposition, the Krull intersection theorem, and the principal ideal theorem hold for *w-ideals ofD. For the case of ★=υ,★wis thew-operation introduced by Wang Fanggui and R.L. McCasland.

ISSN:0092-7872    

DOI:10.1080/00927870008826970

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

In this paper, we generalize the concepts of (intra-, left, right, completely) π-regular semigroups without order to po-semigroups and discuss characterizations and relationships concerning them. Moreover, we introduce the concepts of nil-extensions of po-semigroups first, then consider properties and characterizations of po-semigroups which are nil-extensions of (left, rightt-) simple (π-regular) po-semigroups and complete semilattices of this class of po-semigroups.

ISSN:0092-7872    

DOI:10.1080/00927870008826971

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826972

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826973

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826974

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor