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A characterization of reduced incidence algebras

1981
*
Discrete Mathematics
*

, Rota & Stanley [2] in terms

doi:10.1016/0012-365x(81)90061-3
fatcat:kqrongrje5glpaih47hnxlzugi
*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' ...##
###
A Galois connection for reduced incidence algebras

1974
*
Proceedings of the American Mathematical Society
*

One

doi:10.1090/s0002-9939-1974-0363946-3
fatcat:5slffex2xba3xfajjsrqjkz324
*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 ...##
###
A Galois Connection for Reduced Incidence Algebras

1974
*
Proceedings of the American Mathematical Society
*

One

doi:10.2307/2040058
fatcat:5vpoq4v35zax3ehur3u3warmye
*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 ...##
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Towards the critical problem: on the coalgebraic relation between sets and multisets

1993
*
Discrete Mathematics
*

After studying this new coalgebra (in fact,

doi:10.1016/0012-365x(93)90058-2
fatcat:txfmr23gq5fplbdsqobxo3vzey
*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. ...##
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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. ...##
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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

1991
*
Linear Algebra and its Applications
*

Finite dimensional

doi:10.1016/0024-3795(91)90114-c
fatcat:mybv2t6dovemndy4c5lz4hs6ue
*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. ...##
###
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

2017
*
Bulletin de la Société des sciences et des lettres de Lódz
*

The notion

doi:10.26485/0459-6854/2017/67.1/5
fatcat:2ipai4s4ifcavfrk6zsmoc2yge
*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 . ...##
###
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

1987
*
Journal of combinatorial theory. Series A
*

We introduce the notion

doi:10.1016/0097-3165(87)90006-9
fatcat:o6f2niacsbas3cad7izz7pmxta
*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. ...##
###
Algebras defined by patterns of zeros

1970
*
Journal of Combinatorial Theory
*

One special corollary is that, if V(T) consists

doi:10.1016/s0021-9800(70)80064-3
fatcat:3iupsay47rb4dhbtrrperlfw2q
*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*. ...##
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Preface: Geometric and algebraic combinatorics

2012
*
Designs, Codes and Cryptography
*

On one hand it can be

doi:10.1007/s10623-012-9701-7
fatcat:ucoc7lfxvzdw7bbngw7ncfvvlq
*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. ...
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