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Matrices generated by semilattices
1995
Discrete Applied Mathematics
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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
2010
Filomat
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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
2013
International Journal of Algebra
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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]
2020
arXiv
pre-print
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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
2018
Linear Algebra and its Applications
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2017 pre-print arXiv:1705.05169v1 fatcat:fokpk6hnnzdsznthshmg7bshniOther Versions
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
1996
Linear Algebra and its Applications
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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
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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
2008
Linear Algebra and its Applications
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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
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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
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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
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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]
2019
arXiv
pre-print
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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]
2017
arXiv
pre-print
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., 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
1972
Pacific Journal of Mathematics
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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
2014
International Journal of Contemporary Mathematical Sciences
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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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