Showing papers in "Communications in Algebra in 1994"
TL;DR: In this paper, Locally finitely presented additive categories are defined and discussed in terms of additive categories in algebraic algebraic programs. Communications in Algebra: Vol. 22, No. 5, pp. 1641-1674.
Abstract: (1994). Locally finitely presented additive categories. Communications in Algebra: Vol. 22, No. 5, pp. 1641-1674.
261 citations
TL;DR: An associative ring R with identity is semiperfect if and only if every element of R is a sum of a unit and an idempotent, and R contains no infinite set of orthogonal idempotsents.
Abstract: An associative ring R with identity is semiperfect if and only if every element of R is a sum of a unit and an idempotent, and R contains no infinite set of orthogonal idempotents. A ring which contains no infinite set of orthogonal idempotents is an exchange ring if and only if every element is a sum of a unit and an idempo-tent
208 citations
177 citations
TL;DR: A q-analog for the virasoro algebra was proposed in this paper, where the q is a q-approximation of the q-algebraic relation.
Abstract: (1994). A q-analog for the virasoro algebra. Communications in Algebra: Vol. 22, No. 10, pp. 3755-3774.
99 citations
TL;DR: In this paper, the authors define families of non-noetherian rings and Parameterizing families of Non-Noetherian Ring Parameterization (PNP) is proposed.
Abstract: (1994). Parameterizing families of non-noetherian rings. Communications in Algebra: Vol. 22, No. 10, pp. 3997-4011.
98 citations
TL;DR: In this paper, it was shown that the stable category mod p(F) has a left triangulated structure for F-projective modules, and dual statements for the case of F-injective modules are also true.
Abstract: Let modA be the category of finitely generated right A-modules over an artin algebra ⋀, and F be an additive subfunctor of . Let P(F) denote the full sucategory of A with objects the F-projective modules. If the functor F has enough F- projectives, then we show that the stable category mod p(F)⋀ has a left triangulated structure. In case , the above statement implies that the stable category mod p⋀ has a left triangulated structure. Dual statements for the case of F-injective modules are also true
93 citations
TL;DR: In this article, the Cleft extensions for a hopf algebra generated by a nearly primitive element are presented. But the extensions are not extended to a hop-f-algebra with nearly primitive elements.
Abstract: (1994). Cleft extensions for a hopf algebra generated by a nearly primitive element. Communications in Algebra: Vol. 22, No. 11, pp. 4537-4559.
85 citations
TL;DR: In this paper, the Schutzenberger product of two monoids, the Bruck-Reilly extension of a monoid, strong semilattices of monoid and Rees matrix semigroups of monoids are presented.
Abstract: Presentations are found for the wreath product of two monoids, the Schutzenberger product of two monoids, the Bruck-Reilly extension of a monoid, strong semilattices of monoids and Rees matrix semigroups of monoids.
64 citations
TL;DR: In this article, it was shown that the probability of two randomly chosen elements of a finite-dassical simple group G actually generating G tends to 1 as lei increases.
Abstract: In [KL] it is provcd that the probability of two randomly chosen elements of a finite dassical simple group G actually generating G tends to 1 as lei increases. If gEe, let Pu(g) be the probability that, if h is chosen randomly in G, then (g, h) IG. Let PG : = ma..x{Pu(g) I 9 E e#}. In [KL, Conjecture 2] it is suggested that a stronger result might hold: Pc ---4 0 as IGI ---4 00 for simple classical groups G. In this paper we investigate this question. It turns out that there is an interesting dichotomy here: while the answer is positiw~ whcn the defining dimension is fixed and the field size increases, this is not so
61 citations
TL;DR: In this paper, the authors examined further properties of the replicable functions defined in [MOM] and characterized in [ACMS] and examined the properties of these functions in terms of their repliability properties.
Abstract: We examine further properties of the replicable functions defined in [MOM] and characterized in [ACMS].
59 citations
TL;DR: In this article, the authors define automorphisms of finite groups and show that they can be expressed as a set of automata, i.e., automata of infinite groups.
Abstract: (1994). Automorphisms of finite groups. Communications in Algebra: Vol. 22, No. 15, pp. 6259-6271.
TL;DR: In this article, the minimal subgroups of a finite group G are studied and sufficient conditions for G to be p-milpotent and supersolvable are given for the normalizes of Sylow subgroups.
Abstract: In this paper, the minimal subgroups of a finite group G are studied. Using the normalizes of Sylow subgroups of G, we obtain some sufficient conditions for G to be p-milpotent and supersolvable, which ae extensions of the related results of Burnside, Ito, Buckley and Asaad.
TL;DR: A simple undirected graph X is said to be ½-transitive if the automorphism group AutX of X acts transitively on the vertices and edges, but not on the arcs of X.
Abstract: A simple undirected graph X is said to be ½-transitive if the automorphism group AutX of X acts transitively onthe vertices and edges, but not on the arcs of X. In this pape we determine all ½-transitive graphs of order a product of two distinct primes
TL;DR: In this article, Quotient spaces for hopf algebras are defined and discussed in the context of Hopf Algebra (HAL) and hopf algebra.
Abstract: (1994). Quotient spaces for hopf algebras. Communications in Algebra: Vol. 22, No. 7, pp. 2503-2523.
TL;DR: In this paper, the additive group on complex affine three space admits equivariant trivializations with quotient isomorphic to complex two space, and an additive group action on complex seven space with a non-fmitely generated ring of invariants is presented.
Abstract: All proper rational actions of the additive group on complex affine three space admit equivariant trivializations with quotient isomorphic to complex two space An example of an additive group action on complex seven space with a nonfmitely generated ring of invariants is presented
TL;DR: In this paper, the authors define a class of selfinjective special biserial algebras that are stably equivalent to selfinjectional special Biserials.
Abstract: (1994). Algebras stably equivalent to selfinjective special biserial algebras. Communications in Algebra: Vol. 22, No. 4, pp. 1127-1160.
TL;DR: In this paper, complete lie algebras and heisenberg algesas are discussed. But they do not cover the complete set of complete lie and complete lie graphs.
Abstract: (1994). Complete lie algebras and heisenberg algebras. Communications in Algebra: Vol. 22, No. 13, pp. 5509-5524.
TL;DR: In this article, a detailed study of the geometric hyperplanes of the two generalized hexagons of order (2,2) is presented, which leads to concrete descriptions of th universal embeddings of these hexagons, as well as a description of the G 2 2 -orbits on the Lie algebra g 2 2(2).
Abstract: We present a detailed study of the geometric hyperplanes of the two generalized hexagons of order (2,2). This leads to concrete descriptions of th universal embeddings of these hexagons, as well as a description of the G 2(2)-orbits on the Lie algebra g 2(2), illustrating some of the anomalies of this algebra. As a byproduct of our investigations, we develop some general theory that can be applied to other incidence systems with 3 points per line.
TL;DR: In this paper, it was shown that (rad(modA))2 = 0 implies that A is of finite representation type, and it is well known that an artin algebra A is a finite algebra if and only if red(mod A) = 0.
Abstract: It is well known that an artin algebra A is of finite representation type if and only if red(modA)=0. In this note we deepen this result by showing that(rad(modA))2=0 implies that A is of finite representation type.
TL;DR: A note on the finitistic dimension conjecture is given in this paper, where it is shown that the dimension conjecture can be reduced to the following conjecture: 1 − 1 − 2.
Abstract: (1994). A note on the finitistic dimension conjecture. Communications in Algebra: Vol. 22, No. 7, pp. 2525-2528.
TL;DR: In this article, the authors extend the Tannaka-Krein duality results (over a field) to the non-commutative situation and establish a 1-1 corresponde:ice between tensorial autonomous categories equipped with a "fibre functor".
Abstract: Inspired by a recent paper by Deligne [2], we extend the Tannaka-Krein duility results (over a field) to the non-commutative situation. To be precise, we establish a 1-1 corresponde:ice between ‘tensorial autonomous categories’ equipped with a ‘fibre functor’ (i. e. tannakian categories without the commutativity condition on the tensor product), and ‘quantum groupoids’ (as defined by Maltsiniotis, [9]) which are ‘transitive’ (7.1.). When the base field is perfect, a quantum groupoid over Spec B is transitive iff it is projective and faithfully fiat over B⊗ k B. Moreover, the fibre functor is unique up to ‘quantum isomorphism’ (7.6.). Actually, we show Tannaka-Krein duality results in the more general setting where there is no monoidal structure on the category (and the functor); the algebraic object corresponding to such a category is a ‘semi-transitive’ coalgebroid (5.2. and 5.8.).
TL;DR: In this paper, it was shown that the multiparameter quantum group defined by Reshetikhin and De Concini-Kac-Procesi are indeed equivalent to a Borel-type sub-Hopf-algebra.
Abstract: After Drinfe'd and Jimbo construction [3,7] of quantized universal envelop¬ing algebra associated to each complex simple Lie algebra, larger classes of quasitriangular Hopf algebras as been founded [1,12] and studied [8]. We prove that the multiparameter quantum group defined by Reshetikhin and De Concini-Kac-Procesi are indeed equivalent. Besides we write this algebra as the quantum double of a Borel-type sub-Hopf-algebra