Showing papers in "Communications in Algebra in 1979"
TL;DR: In this paper, Bertini theorems for hypersurface sections containing a subscheme are given for the case of hypersurfaces containing a single subspace and a single component.
Abstract: (1979). Bertini theorems for hypersurface sections containing a subscheme. Communications in Algebra: Vol. 7, No. 8, pp. 775-790.
153 citations
TL;DR: In this article, a model of isotropic simple lie algebras is proposed, which is a generalization of the simple lie algebraic model presented in this paper.
Abstract: (1979). Models of isotropic simple lie algebras. Communications in Algebra: Vol. 7, No. 17, pp. 1835-1875.
84 citations
65 citations
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TL;DR: In this paper, the authors studied Krull domains graded by an arbitrary torsionless grading monoid г and gave necessary and sufficient conditions for A[A] to be a Krull domain and showed that C1(A) is generated by the classes of the homogeneous height-one prime ideals of A.
Abstract: In this paper we study Krull domains graded by an arbitrary torsionless grading monoid г. We generalize many of the well-known results for Krull domains graded by the integers. If г⊂(-г)=0, then there is an injection C1(A0)→C1(A), which need not be a homorphism. We show that C1(A) is generated by the classes of the homogeneous height-one prime ideals of A. Probably the most natural г-graded domain is A[г]. Let A be a Krull domain with quotient field K. If A[г] is a Krull domain, then C1(A[г])=C1(A)⊕C1(K[г]) and C1(K[г]) is independent of K. If г is finitely generated, we give necessary and sufficient conditions or г for A[г] to be a Krull domain. In this case A[г] is just a subring of some generated by monomials. We also study graded domains in which all nonzero homogeneous elements are units. Such graded domains are very close to being group rings over a field.
63 citations
TL;DR: In this article, the springer representations of the weyl groups of classical algebraic groups are studied and the authors show that the springers of these groups can be used to represent algebraic classes.
Abstract: (1979). On the springer representations of the weyl groups of classical algebraic groups. Communications in Algebra: Vol. 7, No. 16, pp. 1713-1745.
62 citations
59 citations
TL;DR: Character tables for all the 56 non-abelian simple groups of order up to 106, including three tables for the family PSL(2,q) and twenty tables for individual groups (with some overlap) are presented in this article.
Abstract: Character tables are presented for all the 56 non-abelian simple groups of order up to 106, including three tables for the family PSL(2,q) and twenty tables for individual groups (with some overlap). Information presented includes the power maps, the orders of the centralizers of elements, and tables of structure constants for each class of involutions.
53 citations
35 citations
TL;DR: Indecomposable division algebras have been studied in this paper, where the authors propose Indecompositionable Division Algebra (IDA) as an algebraic solution to the division problem.
Abstract: (1979). Indecomposable division algebras. Communications in Algebra: Vol. 7, No. 8, pp. 791-817.
35 citations
TL;DR: In this article, it was shown that for any integral doma in A with quotient filed K and for any positive integer n define Int, with certain restrictions placed on A and with n = 1, Int(A, 1) is a Prufer domain.
Abstract: For any integral doma in A with quotient filed K and for any positive integer n define Int .We show that, with certain restrictions placed on A and with n = 1, Int(A,1) is a Prufer domain and we use this to prove the following theorem: If I, J are finitely generated idelas in Int(a,1) satisfying I(a) = J(a) for every a∊A, then I = J.
34 citations
TL;DR: In this article, the central closure of semiprime non-associative rings is discussed and discussed in the context of algebraic topology and non-asymptotics.
Abstract: (1979). Central closure of semiprime non-associative rings. Communications in Algebra: Vol. 7, No. 11, pp. 1103-1132.
TL;DR: Some theorems on the k-theory of coherent sheaves are given in this paper, with a focus on the K-theoretic properties of coherent heaves.
Abstract: (1979). Some theorems on the k-theory of coherent sheaves. Communications in Algebra: Vol. 7, No. 14, pp. 1489-1508.
TL;DR: In this article, partial orders on a field and valuation ring are discussed, and a partial order on the valuation ring is proposed. But the partial order is not a complete order.
Abstract: (1979). Partial orders on a field and valuation rings. Communications in Algebra: Vol. 7, No. 18, pp. 1933-1976.
TL;DR: In this paper, the isomorphism classes of simple groups of order up to 106 distinct from PSL(2,q) are presented in the form G = where m is minimal (with respect to a) and complete in the sense that any pair of generators of G satisfying the relations a2 = bm = 1, with m minimal, will satisfy the defining relations of just one presentation listed here.
Abstract: Of the 56 isomorphism classes of simple groups of order up to 106 there are 10 of order up to 105 distinct from PSL(2,q). Presentations for these groups are given here in the form G = where m is minimal (with respect to a). They are complete in the sense that any pair (a, b) of generators of G satisfying the relations a2 = bm = 1, with m minimal, will satisfy the defining relations of just one presentation listed here.
TL;DR: In this article, Bezout rings and serial rings are discussed and discussed in the context of algebraic communication in algebraic networks, and a discussion of serial rings is presented.
Abstract: (1979). Bezout rings and serial rings. Communications in Algebra: Vol. 7, No. 5, pp. 533-545.
TL;DR: For weakly ideal invariant rings satisfying |R/P |l = | R/p |r for all prime ideals P, the clans are Krull homogeneous and can be characterized by various kinds of links as discussed by the authors.
Abstract: We give an new proof for the main theorem of [8], ie. that a right-noetherian right-a-homogeneous right-weakly ideal invariant ring has a right-artinian classical right-quotient ring, relating it to the a-tors-ion theory; and we show that for weakly ideal invariant rings satisfying | R/P |l = | R/P |r for all prime ideals P , the clans are Krull homogeneous and can be characterized by various kinds of links.
TL;DR: In this paper, generic flatness and the nullstellensatz for ore extensions are discussed and discussed in terms of the nullness of flatness in the context of algebraic structures.
Abstract: (1979). Generic flatness and the nullstellensatz for ore extensions. Communications in Algebra: Vol. 7, No. 3, pp. 259-277.
TL;DR: In this article, Catanese et al. considered severi's proof of the double point formula and showed that severi was not the first to prove the double-point formula.
Abstract: ISSN: 0092-7872 (Print) 1532-4125 (Online) Journal homepage: http://www.tandfonline.com/loi/lagb20 On severi's proof of the double point formula F. Catanese To cite this article: F. Catanese (1979) On severi's proof of the double point formula , Communications in Algebra, 7:7, 763-773, DOI: 10.1080/00927877908822373 To link to this article: http://dx.doi.org/10.1080/00927877908822373 Published online: 27 Jun 2007.
Abstract: We characterize well-ordered sets to be exactly the totally ordered sets whose category of K-linear representations is pure semisimple for any field K. Using this result we exhibit for each natural number n and for n =∞ a ringoid of left pure global dimension 0 and right pure global dimension n.
TL;DR: In this paper, another condition equivalent to de morgan's law is defined, which is a condition that is equivalent to the condition in this paper, and the condition is defined as follows:
Abstract: (1979). Another condition equivalent to de morgan's law. Communications in Algebra: Vol. 7, No. 12, pp. 1309-1312.