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Matrices generated by semilattices

Johan Karlander
1995 Discrete Applied Mathematics  
We give a characterization of O-l matrices M which are generated by semilattices in the way that Mij = 0 if and only if xi A xj = 0 where xi, xj, d are elements in a semilattice. 0166-21 SX/95/SO9.50 6  ...  The generalization is that we consider matrices generated not merely by atomic semilattices but by atomic partially ordered sets.  ...  In Section 3 we then present two characterization theorems: one for matrices generated by atomic partially ordered sets; one for matrices generated by atomic semilattices.  ... 
doi:10.1016/0166-218x(93)e0159-v fatcat:pjoxl6b77zf2thgujluls3hxgm

Bands of λ-simple semigroups

Stojan Bogdanovic, Zarko Popovic, Miroslav Ciric
2010 Filomat  
In the present paper we give characterizations of various special types of bands of λ-semigroups and semilattices of matrices of λ-semigroups.  ...  Semilattices of matrices of λ-simple semigroups are described by Theorem 3. The characterizations of semilattices of hereditary weakly left Archimedean semigroups are given by Theorem 5.  ...  Semilattices of matrices of λ-simple semigroups By the well-known result of A. H. Clifford, any band of λ-simple semigroups is a semillatice of matrices of λ-simple semigroups.  ... 
doi:10.2298/fil1004077b fatcat:rrvww3juxbbypdnj2a3fan3iya

On faithful representations of finite semigroups S of degree |S| over the fields

A. Nagy
2013 International Journal of Algebra  
By a representation of a semigroup S of degree n over a field F we mean a homomorphism γ of S into the multiplicative semigroup of the algebra M n (F) of all n × n matrices with entries in F.  ...  In this paper we focus our attention to the dimension of the subalgebra of M n (F) generated by γ(S), where S is an n-element semigroup and γ is a faithful representation of S of degree n over a field  ...  ) generated by S is k.  ... 
doi:10.12988/ija.2013.13012 fatcat:af4sm27q35gjtam3ehowmeoeba

Positive definite functions on semilattices [article]

Vesa Kaarnioja and Pentti Haukkanen and Pauliina Ilmonen and Mika Mattila
2020 arXiv   pre-print
We introduce a notion of positive definiteness for functions f:P→R defined on meet semilattices (P,≼,∧) and prove several properties for these functions.  ...  In addition, we utilize the LDL^ T decomposition of meet matrices in order to explore the properties of multivariate positive definite arithmetic functions f:Z_+^d→R.  ...  This definition can be expressed in terms of generalized Smith matrices. Theorem 4.2.  ... 
arXiv:1804.03047v2 fatcat:lod22x7xmjfbpc5bmxp2t26uou

Generalized eigenvalue problems for meet and join matrices on semilattices

Pauliina Ilmonen, Vesa Kaarnioja
2018 Linear Algebra and its Applications  
We study generalized eigenvalue problems for meet and join matrices with respect to incidence functions on semilattices.  ...  We provide new bounds for generalized eigenvalues of meet matrices with respect to join matrices under very general assumptions.  ...  In this work, we conduct a first study of generalized eigenvalues of meet and join matrices with respect to incidence functions on semilattices and we provide new bounds for both minimal and dominant eigenvalues  ... 
doi:10.1016/j.laa.2017.09.023 fatcat:ymycjd4aqvfwpnaa36ckjmaq3i

On meet matrices on posets

Pentti Haukkanen
1996 Linear Algebra and its Applications  
We consider meet matrices on posets as an abstract generalization of greatest common divisor (GCD) matrices.  ...  Some of the most important properties of GCD matrices are presented in terms of meet matrices. 0 Ekevier Science Inc., 1996  ...  DEFINITION OF MEET MATRICES Let (P, <) be a finite poset. We call P a meet semilattice [I7, p.  ... 
doi:10.1016/0024-3795(95)00349-5 fatcat:nlbkbtpsinfgvf4v53lninh4vy

Page 1682 of Mathematical Reviews Vol. 58, Issue 3 [page]

1979 Mathematical Reviews  
The authors study upper bounds on the sizes of semigroups gener- ated by two randomly chosen nXn Boolean matrices having N entries equal to one.  ...  The average size of the semigroup generated by two random Boolean matrices is also investigated. The authors’ method is closely related to that of P. Erdés and A. Rényi [Studia Sci. Math.  ... 

On eigenvalues of meet and join matrices associated with incidence functions

Pauliina Ilmonen, Pentti Haukkanen, Jorma K. Merikoski
2008 Linear Algebra and its Applications  
Let (P , , ∧) be a locally finite meet semilattice. Let  ...  The order ideal generated by S is defined as ↓S = {z ∈ P | ∃x ∈ S, z x}. Let ↓ S = {w 1 , w 2 , . . . , w m }, with w i w j ⇒ i j . Let f be a complex-valued function on P .  ...  The dual order ideal generated by S is defined as ↑ S = {z ∈ P | ∃x ∈ S, x z}. Let ↑ S = {w 1 , w 2 , . . . , w m }, with w i w j ⇒ i j . Let f be a complex-valued function on P .  ... 
doi:10.1016/j.laa.2008.04.014 fatcat:cqhkk6haojcqri6asvz6owxf7y

Page 4078 of Mathematical Reviews Vol. 58, Issue 6 [page]

1979 Mathematical Reviews  
Ex- amples include the Mébius algebras introduced by L. Solomon and the semigroup algebras of semilattices studied by D. H. Lehmer.  ...  generalization of the Lehmer-von Sterneck theorem.  ... 

Page 3446 of Mathematical Reviews Vol. , Issue 97F [page]

1997 Mathematical Reviews  
The algebra Lp is generated by the elementary upper triangular matrices z,, having the only nonzero entry, which is 1, in row x and column y for x < y in P.  ...  , Andreja (YU-NOVI-IM; Novi Sad) Representation of finite semilattices by meet-irreducibles.  ... 

Page 966 of Mathematical Reviews Vol. 26, Issue 5 [page]

1963 Mathematical Reviews  
By the maximal semilattice homomorphic image of a semigroup S is meant the semilattice L such that every semilattice homomorphic image of S is also a homo- morphic image of L.  ...  only a finite number of its trans- forms by Gz, from which it follows that G@, is finitely generated.  ... 

Studying the inertias of LCM matrices and revisiting the Bourque-Ligh conjecture [article]

Mika Mattila, Pentti Haukkanen, Jori Mäntysalo
2019 arXiv   pre-print
However, not much more is known about the inertia of LCM matrices in general. The ultimate goal of this article is to improve this situation.  ...  Assuming that S is a meet closed set we define an entirely new lattice-theoretic concept by saying that an element x_i∈ S generates a double-chain set in S if the set meetcl(C_S(x_i))∖ C_S(x_i) can be  ...  In Figure 1 (b) there is a semilattice that has been obtained from an A-set by adding a maximum element x i . By Theorem 2.1 also in this semilattice any element x i generates a double-chain set.  ... 
arXiv:1809.02423v2 fatcat:qd7hrwumsnfd3oingu2niao6iq

On the structure of join tensors with applications to tensor eigenvalue problems [article]

Vesa Kaarnioja
2017 arXiv   pre-print
., a linear combination of rank-1 tensors) and a tensor-train decomposition of join tensors are derived on general join semilattices.  ...  We investigate the structure of join tensors, which may be regarded as the multivariable extension of lattice-theoretic join matrices.  ...  Disclosure statement No potential conflict of interest was reported by the author. Funding The author has been supported by the Academy of Finland under Grant 267789.  ... 
arXiv:1705.06313v1 fatcat:uxnp3yuipvhgfhqrwco65dawtq

On nilpotency and residual finiteness in semigroups

Gérard Lallement
1972 Pacific Journal of Mathematics  
By a result of Malcev, finitely generated semigroups of matrices over a field of characteristic 0 are residually finite [10] .  ...  If a semigroup S is finitely generated, nilpotent, and regular then S is residually finite. Proof. By Proposition 2.3, S is a semilattice of nilpotent groups.  ... 
doi:10.2140/pjm.1972.42.693 fatcat:h2byhajacncifjcvslaqnchilm

Finite semigroups whose semigroup algebra over a field has a trivial right annihilator

Attila Nagy, Lajos Ronyai
2014 International Journal of Contemporary Mathematical Sciences  
The set F S×S of all S-matrices over F is an algebra over F under the usual addition and multiplication of matrices and the product of matrices by scalars.  ...  The above construction can be generalized. Let p > 2 be a prime and S be the semigroup of all 2 × 2 matrices over F p whose rank is at most 1. We have |S| = p 3 + p 2 − p.  ... 
doi:10.12988/ijcms.2014.310115 fatcat:nkeg2ev2uzcwtjxwtkr3werbpy
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