共查询到20条相似文献,搜索用时 62 毫秒
1.
Ilya Kapovich 《Transactions of the American Mathematical Society》2002,354(1):335-362
We prove that fully residually free groups have the Howson property, that is the intersection of any two finitely generated subgroups in such a group is again finitely generated. We also establish some commensurability properties for finitely generated fully residually free groups which are similar to those of free groups. Finally we prove that for a finitely generated fully residually free group the membership problem is solvable with respect to any finitely generated subgroup.
2.
3.
4.
Edgar E. Enochs Overtoun M. G. Jenda Jinzhong Xu 《Algebras and Representation Theory》1999,2(3):259-268
Before his death, Auslander announced that every finitely generated module over a local Gorenstein ring has a minimal Cohen–Macaulay approximation. Yoshimo extended Auslander's result to local Cohen–Macaulay rings admitting a dualizing module.Over a local Gorenstein ring the finitely generated maximal Cohen–Macaulay modules are the finitely generated Gorenstein projective modules so in fact Auslander's theorem says finitely generated modules over such rings have Gorenstein projective covers. We extend Auslander's theorem by proving that over a local Cohen–Macaulay ring admitting a dualizing module all finitely generated modules of finite G-dimension (in Auslander's sense) have a Gorenstein projective cover. Since all finitely generated modules over a Gorenstein ring have finite G-dimension, we recover Auslander's theorem when R is Gorenstein. 相似文献
5.
Anne-Marie Simon 《Algebras and Representation Theory》2009,12(2-5):385-400
The Auslander–Buchweitz theory for finitely generated modules over a Cohen–Macaulay local ring is extended to complete modules, finitely generated or not. This also allows us to extend to complete modules some other known facts concerning finitely generated ones. 相似文献
6.
A finitely generated just-infinite profinite branch group which is not positively finitely generated
Ihor O. Samoilovych 《Archiv der Mathematik》2014,102(3):219-223
We construct a finitely generated profinite branch group which is just-infinite and not positively finitely generated. 相似文献
7.
Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable algebras. First, an example is given to show that the class of finitely generated FA-presentable algebras is not closed under forming finitely generated subalgebras, even within the class of algebras with only unary operations. In contrast, a finitely generated subalgebra of an FA-presentable algebra with a single unary operation is itself FA-presentable. Furthermore, it is proven that the class of unary FA-presentable algebras is closed under forming finitely generated subalgebras and that the membership problem for such subalgebras is decidable. 相似文献
8.
Valeriy G. Bardakov 《代数通讯》2013,41(11):4809-4824
We investigate the palindromic width of finitely generated solvable groups. We prove that every finitely generated 3-step solvable group has finite palindromic width. More generally, we show the finiteness of the palindromic width for finitely generated abelian-by-nilpotent-by-nilpotent groups. For arbitrary solvable groups of step ≥3, we prove that if G is a finitely generated solvable group that is an extension of an abelian group by a group satisfying the maximal condition for normal subgroups, then the palindromic width of G is finite. We also prove that the palindromic width of ??? with respect to the set of standard generators is 3. 相似文献
9.
We show that the subconstruct Fing of Prtop, consisting of all finitely generated pretopological spaces, is the largest Cartesian closed coreflective subconstruct of Prtop. This implies that in any coreflective subconstruct of Prtop, exponential objects are finitely generated. Moreover, in any finitely productive, coreflective subconstruct, exponential objects are precisely those objects of the subconstruct that are finitely generated. We give a counterexample showing that without finite productivity the previous result does not hold. 相似文献
10.
Sarah Campbell 《Journal of Functional Analysis》2005,222(2):292-305
We show that the Hilbert space compression of any (unbounded) finite-dimensional CAT(0) cube complex is 1 and deduce that any finitely generated group acting properly, co-compactly on a CAT(0) cube complex is exact, and hence has Yu's Property A. The class of groups covered by this theorem includes free groups, finitely generated Coxeter groups, finitely generated right angled Artin groups, finitely presented groups satisfying the B(4)-T(4) small cancellation condition and all those word-hyperbolic groups satisfying the B(6) condition. Another family of examples is provided by certain canonical surgeries defined by link diagrams. 相似文献
11.
We extend the concept of presentation of finitely generated commutative monoids to ideals of finitely generated commutative monoids and give algorithms to obtain information about an ideal from a given presentation. 相似文献
12.
Pierre Antoine Grillet 《Semigroup Forum》1972,4(1):242-247
All finitely generated commutative semigroups which do not have proper finite subdirect decompositions are determined. This
yields subdirect decompositions of finitely generated commutative semigroups and some idea of their structure. 相似文献
13.
We introduce the concept of presentation for subsemigroups of finitely generated commutative semigroups, which extends the
concept of presentation for finitely generated commutative semigroups. We show that for every subsemigroup of a finitely generated
commutative semigroup there are special presentations which solve the word problem in the given subsemigroup. Some properties
like being cancellative, reduced and/or torsion free are studied under this new point of view.
This paper was supported by the project DGES PB96-1424. 相似文献
14.
Gábor Tardos 《Order》1986,3(3):211-218
There is only one maximal clone on a set of at most eight elements which has not been known to be finitely generated. We show that it is not finitely generated. 相似文献
15.
M.A.E.H. Sherif 《Algebra Universalis》1997,37(1):70-76
This paper answers a question of H. P. Sankappanavar who asked whether the theory of orthomodular lattices is recursively
(finitely) inseparable (question 9 in [10]). A very similar question was raised by Stanley Burris at the Oberwolfach meeting
on Universal Algebra, July 15–21, 1979, and was later included in G. Kalmbach’s monograph [6] as the problem 42. Actually
Burris asked which varieties of orthomodular lattices are finitely decidable. Although we are not able to give a full answer
to Burris’ question we have a contribution to the problem. Note here that each finitely generated variety of orthomodular
lattices is semisimple arithmetical and therefore directly representable. Consequently each such a variety is finitely decidable.
(For a generalization of this, i.e. a characterization of finitely generated congruence modular varieties that are finitely
decidable see [5].) In section 3, we give an example of finitely decidable variety of orthomodular lattices that is not finitely
generated.
Received June 28, 1995; accepted in final form June 27, 1996. 相似文献
16.
We prove nilpotency of the alternator ideal of a finitely generated binary (-1,1)-algebra. An algebra is a binary (-1,1)-algebra if its every 2-generated subalgebra is an algebra of type (-1,1). While proving the main theorem we obtain various consequences: a prime finitely generated binary (-1,1)-algebra is alternative; the Mikheev radical of an arbitrary binary (-1,1)-algebra coincides with the locally nilpotent radical; a simple binary (-1,1)-algebra is alternative; the radical of a free finitely generated binary (-1,1)-algebra is solvable. Moreover, from the main result we derive nilpotency of the radical of a finitely generated binary (-1,1)-algebra with an essential identity. 相似文献
17.
Peter Kálnai 《代数通讯》2019,47(1):88-100
We (re)introduce four ideal-related generalizations of classic module-theoretic notions: the ideal-superfluity, projective ideal-covers, the ideal-projectivity, and ideal-supplements. For a superfluous ideal I, the main theorem asserts the equivalence between the conditions: “I-supplements are direct summands in finitely generated projective modules”; “finitely generated I-projective modules are projective”; “projective modules with finitely generated factors modulo I are finitely generated”; “finitely generated flat modules with projective factors modulo I are projective.” Moreover, we provide a property of the ideal I which is sufficient for the equivalence to hold true. The property is expressed in terms of idempotent-lifting in matrix rings. 相似文献
18.
Letk be an integer greater than 1 andS be a finitely generated semigroup. The following propositions are equivalent: 1) the semigroup of non negative integers is
not uniformlyk-repetitive; 2) any finitely generated and uniformlyk-repetitive semigroup is finite. As a consequence we prove that any finitely generated and uniformly 4-repetitive semigroup
is finite. 相似文献
19.
Selecta Mathematica - We show that every finitely generated conical refinement monoid can be represented as the monoid $$\mathcal V (R)$$ of isomorphism classes of finitely generated projective... 相似文献
20.
《Advances in Mathematics》1987,64(1):51-85
The set of fixed points of an automorphism of a finitely generated free group is a finitely generated group, settling a conjecture of G. P. Scott's. 相似文献