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Silvia Pianta

Bio: Silvia Pianta is an academic researcher from Catholic University of the Sacred Heart. The author has contributed to research in topics: Commutative property & Projective space. The author has an hindex of 6, co-authored 35 publications receiving 111 citations.

Papers
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Journal ArticleDOI
01 Jan 2010
TL;DR: Generalized Clifford parallelisms involving hyperbolic quadrics in projective spaces over suitable quadratic extensions of F are defined with the help of a quaternion skew field H over a field F of arbitrary characteristic.
Abstract: We define generalized Clifford parallelisms in PG ( 3 , F ) with the help of a quaternion skew field H over a field F of arbitrary characteristic. Moreover we give a geometric description of such parallelisms involving hyperbolic quadrics in projective spaces over suitable quadratic extensions of F .

12 citations

Journal ArticleDOI
TL;DR: In this paper, the correspondence between right loops (P, +) with the property (*) ∀a, b ∈ P : a − (a − b) − b and reflection structures described in [4] is extended to the class of graphs with parallelism.
Abstract: The correspondence between right loops (P, +) with the property “(*) ∀a, b ∈ P : a − (a − b) − b” and reflection structures described in [4] is extended to the class of graphs with parallelism (P, e, ∥). In this connection K-loops correspond with trapezium graphs, i.e. complete graphs with parallelism satisfying two axioms (T1), (T2) (cf. §3 ). Moreover (P, e, ∥ +) is a structure loop (i.e. for each a ∈ P the map a + : P → P; x → a + x is an automorphism of the graph with parallelism (P, e, ∥)) if and only if (P, +) is a K-loop or equivalently if (P, e, ∥) is a trapezium graph.

10 citations

Journal ArticleDOI
TL;DR: In this paper, the authors describe a representation of any semiregular left loop by means of asemiregul bipartite involution set or, equivalently, a 1-factorization (i.e., a parallelism) of a bipartitite graph, with at least one transitive vertex.
Abstract: We describe a representation of any semiregularleft loop by means of asemiregular bipartite involution set or, equivalently, a 1-factorization (i.e., a parallelism) of a bipartite graph, with at least one transitive vertex.

8 citations

Book ChapterDOI
01 Jan 2005
TL;DR: In this article, a general frame for a theory which connects the areas of loops, involution sets and graphs with parallelism is presented, and the main results are stated in §5, §6 and §7.
Abstract: This is a general frame for a theory which connects the areas of loops, involution sets and graphs with parallelism. Our main results are stated in §5, §6 and §7. In §5 we derive a partial binary operation from an involution set and we discuss if such operation is a Bol operation or a K-operation, in §6, we relate involution sets with loops. In §7 we look for the possibility to construct loop-nearrings by considering the automorphism groups of loops.

8 citations


Cited by
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Journal ArticleDOI
TL;DR: In this paper, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
Abstract: This text, drawn from the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-term course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semi-simple rings, Jacobson's theory of the radical representation theory of groups and algebras, prime and semi-prime rings, primitive and semi-primitive rings, division rings, ordered rings, local and semi-local rings, and perfect and semi-perfect rings. By aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation, the author has produced a text which is suitable not only for use in a graduate course, but also for self-study by other interested graduate students. Numerous exercises are also included. This graduate textbook on rings, fields and algebras is intended for graduate students in mathematics.

1,479 citations

Book
01 Jan 2002
TL;DR: In this paper, the value of the variable in each equation is determined by a linear combination of the values of the variables in the equation and the variable's value in the solution.
Abstract: Determine the value of the variable in each equation.

635 citations

Book ChapterDOI
01 Jan 2002
TL;DR: In Part III of this book, it is proved that every Moufang polygon is isomorphic to one of the Moufag polygons described in this chapter.
Abstract: In this chapter, we describe nine families of Moufang polygons. In Part III of this book, we prove that every Moufang polygon is isomorphic to one of the Moufang polygons described in this chapter.

48 citations

Journal ArticleDOI
TL;DR: In this article, a general class of symmetric spaces, called lineated symmetric space (LSS) are defined, which satisfy the axioms of Loos together with an additional axiom that guarantees unique midpoints of symmetry.
Abstract: Abstract We develop the basic theory of a general class of symmetric spaces, called lineated symmetric spaces, that satisfy the axioms of Loos together with an additional axiom that guarantees unique midpoints of symmetry. Our primary interest is the case that these symmetric spaces are Banach manifolds, in which case they exhibit an interesting geometric structure, and particularly in the metric case, where it is assumed the symmetric space carries a convex metric, an invariant complete metric contracting the square root function. One major result is that the distance function between points evolving over time on two geodesics is a convex function. Primary examples arise from involutive Banach-Lie groups (G,σ) admitting a polar decomposition G = P · K, where K is the subgroup fixed by σ and P is the associated symmetric set. We consider an appropriate notion of seminegative curvature for such symmetric spaces endowed with an invariant Finsler metric and prove that the corresponding length metric must be a convex metric. The preceding results provide a general framework for the interesting Finsler geometry of the space of positive Hermitian elements of a C*-algebra that has emerged in recent years.

44 citations

Book ChapterDOI
01 Jan 2015
TL;DR: In this paper, the structural results on certain isometries of spaces of positive definite matrices and on those of unitary groups are put into a common perspective and extend them to the context of operator algebras.
Abstract: Recently we have presented several structural results on certain isometries of spaces of positive definite matrices and on those of unitary groups. The aim of this paper is to put those previous results into a common perspective and extend them to the context of operator algebras, namely, to that of von Neumann factors.

26 citations