Showing papers in "Journal of Algebra in 1974"

TL;DR: Lower bounds on the degree of a Chevalley group over a field of characteristic other than p have been obtained by Landazuri et al. as mentioned in this paper, who showed that for most types of groups and for most primes p it is not difficult to obtain reasonable lower bounds for the complex irreducible characters of G = G(q), using the existence of certain p-subgroups of G resembling extraspecial groups.

TL;DR: In this paper, the authors investigated finitely generated modules and injective modules over fully bounded Noetherian rings and showed that Jacobson's conjecture holds even for commutative Noetherians.

TL;DR: In this article, it was shown that if n > 1 is a positive integer, then every element of R, of all n x n matrices with entries from R is a sum of 2n2 units.

TL;DR: In this paper, it was shown that the class of rings which are almost complete intersections are disjoint, and that they are always Gorenstein rings, which is the case for all rings.

TL;DR: In this article, the authors studied various finiteness conditions on a coalgebra C and the dual algebra C* of all linear functionals on C. They showed that C is a rational coalgebra if every finite function on C* is induced by an element of C. And they showed that any connected coalgebra may be imbedded in the shuffle coalgebra Sh(F) (where si is the space of primitive elements of C).

TL;DR: In this article, the equivalence problem of bilinear forms over a finite dimensional vector space has been solved for symmetric, alternating, and hermitian forms over special fields.

TL;DR: In this article, the authors studied the action of the antipode on the elements of such a basis for a pointed Hopf algebra, and obtained affirmative answers to the second question in case H is pointed and to the first question for H over a field of prime characteristic.

TL;DR: The concept of context-equivalence of rings is introduced and studied in this paper, where a generalization of the Morita Theorems is presented, and induced contexts between quotient rings of R and S are constructed.

TL;DR: In this article, it was shown that Ritt's original proof of Theorem 3 does not make any essential use of the topological manifold structure of the Riemann surface; it consists of combinatorial arguments about extensions of primes to a composite of fields, and depends on the fact that the completion of a field k,(t), at each of its prime spots, is quasifinite when k, is algebraically closed of characteristic 0.

TL;DR: In this article, it was shown that the Gabriel dimension is inherited by a polynomial ring, and upper and lower bounds for this dimension are obtained for the class of modules with Krull dimension.

TL;DR: In this article, the word problem and the divisibility problem are solved and necessary and sufficient conditions for residual finiteness are given for a monoid presented by a single relation.

TL;DR: In this article, a cocommutative, coassociative K-coalgebra with co-it is defined, subject to the requirement that the following diagrams commute: CLC@C where the vertical arrow is the one which switches the factors.

TL;DR: In this paper, it was shown that a Lie subalgebra of a finite dimensional Lie algebra can not be primitive unless it is a nonzero finite-dimensional Lie algebra over a field Fz of characteristic zero.

TL;DR: In this paper, the maximal subalgebras of simple Lie algebra over a finite-dimensional central simple algebra is determined for d/F finite dimensional central simple: associative, associative with involution, alternative, and special (linear) Jordan.

TL;DR: Theorem 3 characterizes all finite groups in which each subgroup is either normal or abnormal as discussed by the authors, and the only subgroup of a group G that is both normal and abnormal in G is G itself.

TL;DR: This inequality was shown to hold for groups of class 2 by I. M. Bride [I], and it was confirmed for metabelian groups in [3] as discussed by the authors.

TL;DR: In this paper, it was shown that all 2-generator groups and all soluble groups have zero presentation rank and that there do not exist any groups with non-zero presentation rank.