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A characterization of reduced incidence algebras

Andreas Kriegl
1981 Discrete Mathematics  
, Rota & Stanley [2] in terms of the convolution and the functions of the incidence algebra).  ...  This paper aims to give a criterium, in terms of the partial ordering on the po-set only, which decides whether or not an equivalence relation on the segments of the po-set is compatible (defined by Doubilet  ...  So we see that such a special choice of q is in gener;\l not possible'  ... 
doi:10.1016/0012-365x(81)90061-3 fatcat:kqrongrje5glpaih47hnxlzugi

A Galois connection for reduced incidence algebras

Robert L. Davis
1974 Proceedings of the American Mathematical Society  
One of the authors' theorems characterized such reduced incidence algebras, among certain subalgebras of the incidence algebra l(P) of a partial order P, in terms of a pointwise multiplication which seems  ...  reduced incidence algebra.  ...  License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use  ... 
doi:10.1090/s0002-9939-1974-0363946-3 fatcat:5slffex2xba3xfajjsrqjkz324

A Galois Connection for Reduced Incidence Algebras

Robert L. Davis
1974 Proceedings of the American Mathematical Society  
One of the authors' theorems characterized such reduced incidence algebras, among certain subalgebras of the incidence algebra l(P) of a partial order P, in terms of a pointwise multiplication which seems  ...  reduced incidence algebra.  ...  License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use  ... 
doi:10.2307/2040058 fatcat:5vpoq4v35zax3ehur3u3warmye

Towards the critical problem: on the coalgebraic relation between sets and multisets

Daniel E. Loeb
1993 Discrete Mathematics  
After studying this new coalgebra (in fact, a Hopf algebra), we characterize the coalgebra of sets within the coalgebra of multisets by its coalgebraic properties.  ...  We introduce a generalization of the coalgebra of sets which we call the coalgebra of multisets.  ...  By the above theorem, the question of biideals reduces itself to the question of nonatomic biideals. We thus have a completely (bi)algebraic characterization of sets among multisets.  ... 
doi:10.1016/0012-365x(93)90058-2 fatcat:txfmr23gq5fplbdsqobxo3vzey

Page 4866 of Mathematical Reviews Vol. , Issue 81M [page]

1981 Mathematical Reviews  
For % finite and x =w the result reduces to the Gould-Gratzer characterization of bounded Boolean powers [M. I. Gould and G. Gratzer, Math. Z. 99 (1967), 16-25; MR 35 #6604].  ...  For a binary compatible relation R on an algebra &=(A,F) the - set [2], := {aE Al(a,z)E R} is called an R-class. While classes of congruence relations have been characterized by A. I.  ... 

Page 2894 of Mathematical Reviews Vol. , Issue 86g [page]

1986 Mathematical Reviews  
Central to the paper is the construction of functors from the full category A of all algebraically compact modules over a ring [resp. from a certain quotient category of A] to a spectral category.  ...  For a (locally finite) pre-ordered set P and a ring R with identity let J(P,R) be the incidence ring of all functions f:P x P — R such that f(z,y) = 0 whenever z ¢ y.  ... 

Page 3614 of Mathematical Reviews Vol. , Issue 2001F [page]

2001 Mathematical Reviews  
Questions of the reducibility of incidence structures in the context of the reducibility of the corresponding structures of independent sets are also studied.  ...  Maurer (H-AOS; Budapest) 2001f:06013 06B05 Walendziak, A. On characterizations of atomistic lattices. (English summary) Algebra Universalis 43 (2000), no. 1, 31-39.  ... 

Universally reflexive algebras

K.R. Fuller, W.K. Nicholson, J.F. Watters
1991 Linear Algebra and its Applications  
Finite dimensional algebras whose representations are all reflexive are characterized as those over which the homomorphisms between any pair of indecomposable projective modules form a vector space of  ...  This includes incidence algebras over finite preordered sets.  ...  If R is a K-algebra, then a left module BM is a bimodule RMK (where km = mk), and this notion of reflexivity reduces to the algebra version.  ... 
doi:10.1016/0024-3795(91)90114-c fatcat:mybv2t6dovemndy4c5lz4hs6ue

Page 510 of Mathematical Reviews Vol. , Issue 86b [page]

1986 Mathematical Reviews  
Drenski, “Minimal basis of identities of a second-order matrix algebra over a field of characteristic zero” (Russian), Algebra i Logika, to appear] that a basis for the identities in M2(K) is formed by  ...  A complete characterization of the square zero radical commutative Artinian rings and finite-dimensional alge- bras over algebraically closed fields that satisfy (#) is given.  ... 

Page 1093 of Mathematical Reviews Vol. 53, Issue 4 [page]

1977 Mathematical Reviews  
reduced incidence algebra.  ...  Theorem 4.1 supplies a characterization of the reduced ——s  ... 

Reduced incidence algebras description of cobweb posets and KoDAGs

Ewa Krot-Sieniawska
2017 Bulletin de la Société des sciences et des lettres de Lódz  
The notion of reduced incidence algebra of an arbitrary cobweb poset is delivered. The incidence algebra combinatorial characterization for an arbitrary positive integers valued sequence is given.  ...  The standard reduced incidence algebra R(Π) is the maximally reduced incidence algebra R(Π), i.e. the smallest reduced incidence algebra on Π.  ...  The the numbers F n (n ≥ 0) are the incidence coefficients in the standard reduced algebra R(Π) of cobweb poset Π uniquely designated by the sequence F = {F n } n≥0 .  ... 
doi:10.26485/0459-6854/2017/67.1/5 fatcat:2ipai4s4ifcavfrk6zsmoc2yge

Page 19 of Mathematical Reviews Vol. , Issue 91E [page]

1991 Mathematical Reviews  
Next a generalisation of an example of Mitchell is treated to con- clude that no combinatorial characterization (independent of the field) exists for posets with incidence algebra of global dimension at  ...  The authors characterize QUnif as the largest final completion of A. They also characterize the universal final completion of A. {For the entire collection see MR 90k:68003.} H.  ... 

Antipodes and incidence coalgebras

William R Schmitt
1987 Journal of combinatorial theory. Series A  
We introduce the notion of a reduced incidence coalgebra of a family of locally finite partially ordered sets and describe how bialgebras and Hopf algebras arise as such coalgebras.  ...  In the case when a reduced incidence coalgebra is a Hopf algebra, we give explicit recursive and closed formulas for the antipode, each of which generalizes a corresponding formula from the theory of Mobius  ...  algebra which is a reduced incidence coalgebra.  ... 
doi:10.1016/0097-3165(87)90006-9 fatcat:o6f2niacsbas3cad7izz7pmxta

Algebras defined by patterns of zeros

Robert L. Davis
1970 Journal of Combinatorial Theory  
One special corollary is that, if V(T) consists of upper triangular (finite or infinite) matrices and contains the identity, then there is such a convolution if and only if V(T) is the incidence algebra  ...  If X is any set and T any subset of X • X, call V(T) the vector space of all functions with support T and values in a field of characteristic zero.  ...  In fact, it is a consequence of the axiomatic characterization of DAVIS incidence algebras given by David A.  ... 
doi:10.1016/s0021-9800(70)80064-3 fatcat:3iupsay47rb4dhbtrrperlfw2q

Preface: Geometric and algebraic combinatorics

Edwin R. van Dam, Willem H. Haemers
2012 Designs, Codes and Cryptography  
On one hand it can be a tool for a better understanding of combinatorial objects, such as error correcting codes, block designs, point-line incidence geometries, and permutation groups.  ...  The present issue of Designs, Codes and Cryptography is devoted to the theme "Geometric and Algebraic Combinatorics". A central concept in this research area is the Association Scheme.  ...  The proof uses a strong form of eigenvalue interlacing to reduce the problem to one about root lattices. 8.  ... 
doi:10.1007/s10623-012-9701-7 fatcat:ucoc7lfxvzdw7bbngw7ncfvvlq
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