共查询到20条相似文献,搜索用时 15 毫秒
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Christian Herrmann 《Algebra Universalis》2013,70(2):163-174
We review (and slightly extend) Bjarni Jónsson’s results on representations of arguesian lattices that are complemented, of low height, or of simple gluing structure. 相似文献
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We show that if P is an infinite poset whose proper order ideals have cardinality strictly less than ${|P|}$ and ${\kappa}$ is a cardinal number strictly less than ${|P|}$ , then P has a principal order ideal of cardinality at least ${\kappa}$ . We apply this result to characterize the possible sizes of unary Jónsson algebras. 相似文献
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We show that, like singular cardinals, and weakly compact cardinals, Jensen's core model K for measures of order zero [4] calculates correctly the successors of Jónsson cardinals, assuming does not exist. Namely, if is a Jónsson cardinal then , provided that there is no non-trivial elementary embedding . There are a number of related results in ZFC concerning in V and inner models, for a Jónsson or singular cardinal.
Received: 8 December 1998 相似文献
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Patrice P. Ntumba 《Ricerche di matematica》2010,59(1):109-124
In an earlier paper of the author, a version of the Witt’s theorem was obtained within a specific subcategory of the category of A{mathcal A}-modules: the full subcategory of convenient A{mathcal A}-modules. A further investigation yields two more versions of the Witt’s theorem by revising the notion of convenient A{mathcal A}-modules. For the first version, the A{mathcal A}-bilinear form involved is either symmetric or antisymmetric, and the two isometric free sub-A{mathcal A}-modules, the isometry between which may extend to an isometry of the non-isotropic convenient A{mathcal A}-module concerned onto itself, are assumed pre-hyperbolic. On the other hand, for the second version, the A{mathcal A}-bilinear form defined on the non-isotropic convenient A{mathcal A}-module involved is set to be symmetric, and the two isometric free sub-A{mathcal A}-modules, whose orthogonals are to be proved isometric, are assumed strongly non-isotropic and disjoint. 相似文献
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David A. Richter 《Advances in Applied Clifford Algebras》2004,14(2):215-224
This note describes a way to realize a “projective” version of Gosset’s 240-vertex semiregular polytope 421 using the Clifford
algebra Cl(8) generated by an 8-dimensional vector space equipped with a non-degenerate quadratic form. The 120 vertices of
this projective Gosset figure are also seen to coincide with a particular basis for the Lie algebra
相似文献
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L. Zádori 《Algebra Universalis》1995,33(2):216-236
We define nonextendible colored posets and zigzags of a poset. These notions are related to the earlier notions of gaps, holes, obstructions and zigzags considered by Duffus, Nevermann, Rival, Tardos and Wille. We establish some properties of zigzags. By using these properties we give a proof of the well known conjecture that states that any finite bounded poset which admits Jsson operations, also admits a near unanimity function. We also provide an infinite poset that shows that we cannot drop the finiteness in this conjecture.Presented by R. McKenzie. 相似文献
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Dynamic algebras are algebraic counterparts of dynamic logics: propositional logical systems endowed with a set of modal
operators. In [18], B. Jónsson introduced dynamic algebras as Boolean algebras with unary operators, the indices of which
range over a given Kleene algebra. On the other hand, V.R. Pratt and D. Kozen proposed a two-sorted approach to dynamic algebras,
which was followed in the early papers on the topic, such as Fischer and Ladner [15] and Németi [28]. For a recent overview
of the field cf. [4]. In the present paper we investigate connections (as well as diversities) between these two approaches.
Our main aim is to transfer (where possible) two-sorted results on separability and decidability to the one-sorted case and
to extend them to broad classes of varieties of Jónsson dynamic algebras. In particular, as a consequence of such considerations,
we obtain a decidability result on Kleene algebras. 相似文献
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We give many examples of applying Bogoliubov’s forest formula to iterative solutions of various nonlinear equations. The same
formula describes an extremely wide class of objects, from an ordinary quadratic equation to renormalization in quantum field
theory.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 316–343, February, 2008. 相似文献
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Patrick R. Girard 《Advances in Applied Clifford Algebras》1999,9(2):225-230
Einstein’s equations of the general theory of relativity are rewritten within a Clifford algebra. This algebra is otherwise
isomorphic to a direct product of two quaternion algebras. A multivector calculus is developed within this Clifford algebra
which differs from the corresponding complexified algebra used in the standard spacetime algebra approach. 相似文献
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Hans-E. Porst 《Journal of Pure and Applied Algebra》2012,216(8-9):1768-1774
Takeuchi’s famous free Hopf algebra construction is analyzed from a categorical point of view, and so is the construction of the Hopf envelope of a bialgebra. Both constructions in fact can be described as compositions of well known and natural constructions. This way certain partially wrong perceptions of these constructions are clarified and their mutual relation is made precise. The construction of Hopf envelopes finally is shown to provide a construction of a Hopf coreflection of bialgebras by simple dualization. The results provided hold for any commutative von Neumann regular ring, not only for fields. 相似文献
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The equational complexity of Lyndon’s nonfinitely based 7-element algebra lies between n − 4 and 2n + 1. This result is based on a new algebraic proof that Lyndon’s algebra is not finitely based. We prove that Lyndon’s algebra
is inherently nonfinitely based relative to a rather rich class of algebras. We also show that the variety generated by Lyndon’s
algebra contains subdirectly irreducible algebras of all cardinalities except 0, 1, and 4. 相似文献
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The bcβγ-system $ \mathcal{W} $ of rank 3 has an action of the affine vertex algebra $ {V_0}\left( {\mathfrak{s}{{\mathfrak{l}}_2}} \right) $ , and the commutant vertex algebra $ \mathcal{C}=\mathrm{Com}\left( {{V_0}\left( {\mathfrak{s}{{\mathfrak{l}}_2}} \right),\mathcal{W}} \right) $ contains copies of V ?3/2 $ \left( {\mathfrak{s}{{\mathfrak{l}}_2}} \right) $ and Odake’s algebra $ \mathcal{O} $ . Odake’s algebra is an extension of the N = 2 super-conformal algebra with c = 9, and is generated by eight fields which close nonlinearly under operator product expansions. Our main result is that V ?3/2 $ \left( {\mathfrak{s}{{\mathfrak{l}}_2}} \right) $ and $ \mathcal{O} $ form a Howe pair (i.e., a pair of mutual commutants) inside $ \mathcal{C} $ . More generally, any finite-dimensional representation of a Lie algebra $ \mathfrak{g} $ gives rise to a similar Howe pair, and this example corresponds to the adjoint representation of $ \mathfrak{s}{{\mathfrak{l}}_2} $ . 相似文献
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Reyer Sjamaar 《Bulletin of the Brazilian Mathematical Society》2011,42(4):783-803
Hans Duistermaat was scheduled to lecture in the 2010 School on Poisson Geometry at IMPA, but passed away suddenly. This is a record of a talk I gave at the 2010 Conference on Poisson Geometry (the week after the School) to share some of my memories of him and to give a brief assessment of his impact on the subject. 相似文献
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Christian Herrmann 《Algebra Universalis》2010,63(1):45-64
Extending work of von Neumann, Jónsson has shown that each complemented modular lattice, L admitting a large partial n-frame with n ≥ 4, or with n ≥ 3 and L Arguesian, can be coordinatized as the lattice of all principal right ideals of some regular ring. His proof built on the
embedding of L into the subgroup lattice of an abelian group which follows from Frink’s embedding of L into to a direct product of subspace lattices of irreducible projective spaces and coordinatization of the latter. We offer
a proof which, in addition to these results, employs only some elementary linear algebra. Luca Giudici’s thesis [6] is an
important source for this approach. 相似文献