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91.
Dan Lee Leanne Leer Shara Pilch Yu Yasufuku 《Proceedings of the American Mathematical Society》2001,129(11):3193-3200
We find necessary and sufficient conditions for a complete local ring to be the completion of a reduced local ring. Explicitly, these conditions on a complete local ring with maximal ideal are (i) or , and (ii) for all , if is an integer of , then .
92.
Moharram A. Khan 《Czechoslovak Mathematical Journal》2000,50(4):791-801
In this paper we investigate commutativity of rings with unity satisfying any one of the properties:
for some f(X) in
and g(X), h(X) in
where m 0, r 0, s 0, n > 0, t > 0 are non-negative integers. We also extend these results to the case when integral exponents in the underlying conditions are no longer fixed, rather they depend on the pair of ring elements x and y for their values. Further, under different appropriate constraints on commutators, commutativity of rings has been studied. These results generalize a number of commutativity theorems established recently. 相似文献
93.
We compute the subdirectly irreducible factors of the free Hermitean (semi)lattice generated by a single element a subject to the relation aa
; we also compute the factors of its induced distributive presentation. 相似文献
94.
V. Yu. Popov 《Mathematical Notes》2000,67(4):495-504
An example of a series of varieties of rings
with the finite basis property is constructed for which the word problem in the relatively free ring
of rankn in the variety
is decidable if and only ifn <p.
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 582–594, April, 2000. 相似文献
95.
K. Varadarajan 《Proceedings Mathematical Sciences》2000,110(2):133-136
Define a ringA to be RRF (respectively LRF) if every right (respectively left)A-module is residually finite. We determine the necessary and sufficient conditions for a formal triangular matrix ring
to be RRF (respectively LRF). Using this we give examples of RRF rings which are not LRF. 相似文献
96.
Olga Polverino 《Designs, Codes and Cryptography》2000,20(3):319-324
In this paper we show that a small minimalblocking set in PG(2,p3), with p 7,is of Rédei type. 相似文献
97.
Philippe Gille 《K-Theory》2000,21(1):57-100
Let G/F be a semisimple algebraic group defined over a field F with characteristic
. Let us denote by
the Galois cohomology group introduced by Kato. If
, we show that the p-primary part of Rost's invariant
lifts in characteristic 0. This result allows to deduce properties of the Rost invariant in positive characteristic from known properties in characteristic 0. The case of Merkurjev–Suslin's invariant is specially interesting, i.e. if G/F=SL(D) for a central simple algebra D/F with degree p and class
, one has
and an element
is a reduced norm if and only if the cup-product
is trivial in
; one characterizes also in positive characteristic fields with p-dimension
by the surjectivity of reduced norms.In a second part, we study Rost invariants when the base field is complete for a discrete valuation. As planned by Serre, invariants are then linked with Bruhat–Tits' theory, this yields a new proof of their nontriviality. 相似文献
98.
Yiqiang Zhou 《Algebra Colloquium》2000,7(3):305-318
For a ring R and a right R-module M, a submodule N of M is said to be -small in M if, whenever N + X = M with M/X singular, we have X = M. If there exists an epimorphism p: P M such that P is projective and Ker(p) is -small in P, then we say that P is a projective -cover of M. A ring R is called -perfect (resp., -semiperfect, -semiregular) if every R-module (resp., simple R-module, cyclically presented R-module) has a projective -cover. The class of all -perfect (resp., -semiperfect, -semiregular) rings contains properly the class of all right perfect (resp., semiperfect, semiregular) rings. This paper is devoted to various properties and characterizations of -perfect, -semiperfect, and -semiregular rings. We define (R) by (R)/Soc(RR) = Jac(R/Soc(RR)) and show, among others, the following results:
The research was partially supported by the NSERC of Canada under Grant OGP0194196.2000 Mathematics Subject Classification: 16L30, 16E50 相似文献
(1) | (R) is the largest -small right ideal of R. |
(2) | R is -semiregular if and only if R/(R) is a von Neumann regular ring and idempotents of R(R) lift to idempotents of R. |
(3) | R is -semiperfect if and only if R/(R) is a semisimple ring and idempotents of R/(R) lift to idempotents of R. |
(4) | R is -perfect if and only if R/Soc(RR) is a right perfect ring and idempotents of R/(R) lift to idempotents of R. |
99.
Hans H. Brungs Joachim Grä ter 《Transactions of the American Mathematical Society》2000,352(7):3357-3379
A subring of a division algebra is called a valuation ring of if or holds for all nonzero in . The set of all valuation rings of is a partially ordered set with respect to inclusion, having as its maximal element. As a graph is a rooted tree (called the valuation tree of ), and in contrast to the commutative case, may have finitely many but more than one vertices. This paper is mainly concerned with the question of whether each finite, rooted tree can be realized as a valuation tree of a division algebra , and one main result here is a positive answer to this question where can be chosen as a quaternion division algebra over a commutative field.
100.
Alessandro Berarducci 《Transactions of the American Mathematical Society》2000,352(2):553-577
The field of generalized power series with real coefficients and exponents in an ordered abelian divisible group is a classical tool in the study of real closed fields. We prove the existence of irreducible elements in the ring consisting of the generalized power series with non-positive exponents. The following candidate for such an irreducible series was given by Conway (1976): . Gonshor (1986) studied the question of the existence of irreducible elements and obtained necessary conditions for a series to be irreducible. We show that Conway's series is indeed irreducible. Our results are based on a new kind of valuation taking ordinal numbers as values. If we can give the following test for irreducibility based only on the order type of the support of the series: if the order type is either or of the form and the series is not divisible by any monomial, then it is irreducible. To handle the general case we use a suggestion of
M.-H. Mourgues, based on an idea of Gonshor, which allows us to reduce to the special case . In the final part of the paper we study the irreducibility of series with finite support.
M.-H. Mourgues, based on an idea of Gonshor, which allows us to reduce to the special case . In the final part of the paper we study the irreducibility of series with finite support.