Finite projective lattices are sharply transferable

1975 ◽  
Vol 5 (1) ◽  
pp. 407-409 ◽  
Author(s):  
Harry Lakser
Keyword(s):  
Projective Lattices

Relative characters for H-projective RG-lattices

1988 ◽  
Vol 104 (2) ◽  
pp. 207-213 ◽  
Author(s):  
Peter Symonds
Keyword(s):  
Representation Theory ◽  
Direct Summand ◽  
Modular Representation ◽  
Dedekind Domain ◽  
Modular Representation Theory ◽  
Trivial Group ◽  
Ordinary Character ◽  
Projective Lattices

If G is a group with a subgroup H and R is a Dedekind domain, then an H-projective RG-lattice is an RG-lattice that is a direct summand of an induced lattice for some RH-lattice N: they have been studied extensively in the context of modular representation theory. If H is the trivial group these are the projective lattices. We define a relative character χG/H on H-projective lattices, which in the case H = 1 is equivalent to the Hattori–Stallings trace for projective lattices (see [5, 8]), and in the case H = G is the ordinary character. These characters can be used to show that the R-ranks of certain H-projective lattices must be divisible by some specified number, generalizing some well-known results: cf. Corollary 3·6. If for example we take R = ℤ, then |G/H| divides the ℤ-rank of any H-projective ℤG-lattice.

Projective Geometries and Projective Lattices

2000 ◽  
pp. 25-53
Author(s):  
Claude-Alain Faure ◽  
Alfred Frölicher
Keyword(s):  
Projective Geometries ◽  
Projective Lattices

Distributive Projective Lattices

1970 ◽  
Vol 22 (3) ◽  
pp. 472-475 ◽  
Author(s):  
Kirby A. Baker ◽  
Alfred W. Hales
Keyword(s):  
Lattice Theory ◽  
Free Lattice ◽  
Important Case ◽  
Distributive Lattices ◽  
Interesting Corollary ◽  
Projective Lattices

Two basic unsolved problems of lattice theory are (1) the characterization of sublattices of free lattices and (2) the characterization of projective lattices. A solution to an important case of the first problem has been provided by Galvin and Jónsson [3], who characterize distributive sublattices of free lattices. In this paper, we solve the same case of the second problem by characterizing distributive projective lattices (Theorem 4.1). An interesting corollary is the verification for distributive lattices of the conjecture that a, finite lattice is projective if and only if it is a sublattice of a free lattice.

scholarly journals Projective lattices of tiled orders

2018 ◽  
pp. 16-19
Author(s):  
V. Zhuravlev ◽  
I. Tsyganivska
Keyword(s):  
Valuation Ring ◽  
Discrete Valuation Ring ◽  
Global Dimension ◽  
Necessary Condition ◽  
Finite Global Dimension ◽  
Irreducible Lattice ◽  
Projective Lattice ◽  
The One ◽  
Projective Lattices ◽  
Tile Order

Tiled orders over discrete valuation ring have been studied since the 1970s by many mathematicians, in particular, by Yategaonkar V.A., Tarsy R.B., Roggenkamp K.W, Simson D., Drozd Y.A., Zavadsky A.G. and Kirichenko V.V. Yategaonkar V.A. proved that for every n > 2, there is, up to an isomorphism, a finite number of tiled orders over a discrete valuation ring O of finite global dimension which lie in $M_n(K)$ where K is a field of fractions of a commutatively discrete valuation ring O. The articles by R.B. Tarsy, V.A. Yategaonkar, H. Fujita, W. Rump and others are devoted to the study of the global dimension of tiled orders. H. Fujita described the reduced tiled orders in Mn(D) of finite global dimension for n = 4; 5. V.M. Zhuravlev and D.V. Zhuravlev described reduced tiled orders in Mn(D) of finite global dimension for n = 6: This paper examines the necessary condition for the finiteness of the global dimension of the tile order. Let A be a tiled order. The kernel of the projective resolvent of an irreducible lattice has the form M1f1 +M2f2 + ::: +Msfs, where Mi is irreducible lattice, fi is some vector. If the tile order has a finite global dimension, then there is a projective lattice that is the intersection of projective lattices. This condition is the one explored in the paper.

Sublattices of free lattices and projective lattices

1995 ◽  
pp. 95-134
Author(s):  
Ralph Freese ◽  
Jaroslav Jezek ◽  
J. Nation
Keyword(s):  
Projective Lattices

scholarly journals Numerical Evidence for a Conjectural Generalization of Hilbert's Theorem 132

2003 ◽  
Vol 6 ◽  
pp. 68-88
Author(s):  
W. Bley
Keyword(s):  
Functional Equation ◽  
Group Ring ◽  
Integral Group Ring ◽  
Integral Group ◽  
Numerical Evidence ◽  
Projective Lattices ◽  
Tate Motives

AbstractThis paper presents an algorithm for computing numerical evidence for a conjecture whose validity is predicted by the requirement that the equivariant Tamagawa number conjectures for Tate motives as formulated by Burns and Flach are compatible with the functional equation of the Artin L-series. The algorithm includes methods for the computation of Fitting ideals and projective lattices over the integral group ring.

scholarly journals Projective lattices and bounded homomorphisms

1972 ◽  
Vol 40 (1) ◽  
pp. 111-119 ◽  
Author(s):  
Alan Kostinsky
Keyword(s):  
Projective Lattices
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