共查询到20条相似文献,搜索用时 15 毫秒
1.
Ahmet A. Husainov 《Semigroup Forum》2011,82(2):261-270
The article is devoted to the global dimension of a R-monoid ring RM(E,I) of a free partially commutative monoid. We prove that if the supremum of numbers of distinct pairwise commuting elements in E is equal to n, then gl dim RM(E,I)=n+gl dim R. Moreover, we get a generalized formula for the global dimensions of the categories of M(E,I)-objects in Abelian categories. 相似文献
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4.
James East 《代数通讯》2013,41(7):2659-2665
5.
Robert Gilmer 《Proceedings of the American Mathematical Society》1999,127(5):1265-1267
We determine equivalent conditions on a commutative Artinian ring in order that the ideal of consisting of polynomials that vanish on should be principal. Our results correct an error in a paper of Niven and Warren.
6.
We first study the quasi-Baerness of R[x; σ, δ] over a quasi-Baer ring R when σ is an automorphism of R, obtaining an affirmative result. We next show that if R is a right principally quasi-Baer ring and σ is an automorphism of R with σ(e) = e for any left semicentral idempotent e ∈ R, then R[x; σ, δ] is right principally quasi-Baer. As a corollary, we have that R[x; δ] over a right principally quasi-Baer ring R is right principally quasi-Baer. Finally, we give conditions under which the quasi-Baernesses (right principal quasi-Baernesses) of R and R[x; σ, δ] are equivalent. 相似文献
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A. V. Kelarev 《Proceedings of the American Mathematical Society》1997,125(7):2191-2193
We give an example of a primitive ring which is a sum of two Wedderburn radical subrings. This answers an open question and simplifies the proof of the known theorem that there exists a ring which is not nil but is a sum of two locally nilpotent subrings.
9.
We first establish the commutativity for the semiprime ring satisfying [x
n
, y]x
r = ±y
s[x, y
m]y
t for all x, y in R, where m, n, r, s, and t are fixed non-negative integers, and further, we investigate the commutativity of rings with unity under some additional hypotheses. Moreover, it is also shown that the above result is true for s-unital rings. Also, we provide some counterexamples which show that the hypotheses of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital. 相似文献
10.
Lattice orders on the semigroup ring of a positive rooted monoid are constructed, and it is shown how to make the monoid ring into a lattice-ordered ring with squares positive in various ways. It is proved that under certain conditions these are all of the lattice orders that make the monoid ring into a lattice-ordered ring. In particular, all of the partial orders on the polynomial ring A[x] in one positive variable are determined for which the ring is not totally ordered but is a lattice-ordered ring with the property that the square of every element is positive. In the last section some basic properties of d-elements are considered, and they are used to characterize lattice-ordered division rings that are quadratic extensions of totally ordered division rings. 相似文献
11.
Manish Kumar 《Proceedings of the American Mathematical Society》2005,133(2):343-348
It is shown that there exists an ordered abelian group that has no smallest positive element and that has no sequence of nonzero elements converging to zero. Some formulae for the rank of ordered abelian groups have been derived and a necessary condition for an order type to be rank of an ordered abelian group has been discussed. These facts have been translated to the spectrum of a valuation ring using some well-known results in valuation theory.
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Friedrich Wehrung 《Algebra Universalis》1999,40(3):247-411
We introduce the dimension monoid of a lattice L, denoted by Dim L. The monoid Dim L is commutative and conical, the latter meaning that the sum of any two nonzero elements is nonzero. Furthermore, Dim L is given along with the dimension map, D\Delta from L2L to Dim L, which has the intuitive meaning of a distance function. The maximal semilattice quotient of Dim L is isomorphic to the semilattice Conc L of compact congruences of L; hence Dim L is a precursor of the congruence lattice of L. Here are some additional features of this construction: ¶¶ (1) Our dimension theory provides a generalization to all lattices of the von Neumann dimension theory of continuous geometries. In particular, if L is an irreducible continuous geometry, then Dim L is either isomorphic to \Bbb Z+\Bbb Z^+ or to \Bbb R+\Bbb R^+.¶ (2) If L has no infinite bounded chains, then Dim L embeds (as an ordered monoid) into a power of \Bbb Z+è{¥}.{\Bbb Z}^{+}\cup \{\infty\}.¶ (3) If L is modular or if L has no infinite bounded chains, then Dim L is a refinement monoid.¶ (4) If L is a simple geometric lattice, then Dim L is isomorphic to \Bbb Z+\Bbb Z^+, if L is modular, and to the two-element semilattice, otherwise.¶ (5) If L is an à0\aleph_0-meet-continuous complemented modular lattice, then both Dim L and the dimension function D\Delta satisfy (countable) completeness properties.¶¶ If R is a von Neumann regular ring and if L is the lattice of principal right ideals of the matrix ring M2 (R), then Dim L is isomorphic to the monoid V (R) of isomorphism classes of finitely generated projective right R-modules. Hence the dimension theory of lattices provides a wide lattice-theoretical generalization of nonstable K-theory of regular rings. 相似文献
14.
Pierre Guillot 《Advances in Mathematics》2005,196(2):276-309
We use the Steenrod algebra to study the Chow ring CH*BG of the classifying space of an algebraic group G. We describe a localization property which relates a given G to its elementary abelian subgroups, and we study a number of particular cases, namely symmetric groups and Chevalley groups. It turns out that the Chow rings of these groups are completely determined by the abelian subgroups and their fusion. 相似文献
15.
Thierry Petit Lobão 《代数通讯》2013,41(12):4407-4412
Let G be a complete monomial group with abelian base, namely, G = AwrSym m , the wreath product of a finite abelian group A with the symmetric group on m letters. Then the group G is determined by its integral group ring. 相似文献
16.
Vesselin Drensky 《代数通讯》2013,41(7):2115-2127
Lret N be a nilpotent of class 2 Lie algebra with one-dimensional centre C = Kc over an infinite field K and let p : N → Endk:(V) be a representation of N in a vector space V such that p(c) is invertible in Endk(V). We find a basis for the identities of the representation p. As consequences we obtain a basis for all the weak polynomial identities of the pair (M2:(K), s12(K)) over an infinite field K of characteristic 2 and describe the identities of the regular representation of Lie algebras related with the Weyl algebra and its tensor powers. 相似文献
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The Bruhat decomposition,Tits system and Iwahori ring for the monoid of matrices over a finite field
Louis Solomon 《Geometriae Dedicata》1990,36(1):15-49
Let G=GL
n
(F
q
) be the finite general linear group and let M=M
n
(F
q
) be the monoid of all n×n matrices over F
q
. Let B be a Borel subgroup of G, let W be the subgroup of permutation matrices, and let W be the monoid of all zero-one matrices which have at most one non-zero entry in each row and each column. The monoid plays the same role for M that the Weyl group W does for G. In particular there is a length function on which extends the length function on W and a C-algebra H
C
(M, B) which includes Iwahori's Hecke algebra H
C
(G, B) and shares many of its properties.For Jacques Tits on his sixtieth birthday 相似文献
19.
Weimin Li 《Semigroup Forum》1994,49(1):143-149
We explicitly find all the idempotents in eachL(R)-class and all the inverses of each element of the strong endomorphism monoid of a graph. The number of these idempotents
and inverses is also obtained.
The author is deeply indebted to Professor Dr. T. E. Hall for his stimulating questions about this theme and much improvement
made to an earlier version of this paper. The author would like to thank Professor Dr. U. Knauer and Dr. E. Wilkeit for helpful
comments. 相似文献
20.
Abdollah Alhevaz 《代数通讯》2017,45(3):919-923
Ever since the introduction, skew inverse Laurent series rings have kept growing in importance, as researchers characterized their properties (such as Noetherianness, Armendarizness, McCoyness, etc.) in terms of intrinsic properties of the base ring and studied their relations with other fields of mathematics, as for example quantum mechanics theory. The goal of our paper is to study the primeness and semiprimeness of general skew inverse Laurent series rings R((x?1;σ,δ)), where R is an associative ring equipped with an automorphism σ and a σ-derivation δ. 相似文献