The 0-distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for 0-distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.
We characterize totally ordered sets within the class of all ordered sets containing at least three-element chains using a simple relationship between their isotone transformations and the so called 2-, 3-, 4-endomorphisms which are introduced in the paper. Another characterization of totally ordered sets within the class of ordered sets of a locally finite height with at least four-element chains in terms of the regular semigroup theory is also given.
The concept of the (dual) binary discriminator was introduced by R. Halas, I. G. Rosenberg and the author in 1999. We study finite algebras having the (dual) discriminator as a term function. In particular, a simple characterization is obtained for such algebras with a majority term function.
Let $G$ be a finite group. Let $X_1(G)$ be the first column of the ordinary character table of $G$. We will show that if $X_1(G)=X_1({\rm PGU}_3(q^2))$, then $G \cong{\rm PGU}_3(q^2)$. As a consequence, we show that the projective general unitary groups ${\rm PGU}_3(q^2)$ are uniquely determined by the structure of their complex group algebras., Farrokh Shirjian, Ali Iranmanesh., and Obsahuje bibliografické odkazy
An inverse semigroup $S$ is pure if $e=e^2$, $a\in S$, $e<a$ implies $a^2=a$; it is cryptic if Green's relation $\mathcal {H}$ on $S$ is a congruence; it is a Clifford semigroup if it is a semillatice of groups. We characterize the pure ones by the absence of certain subsemigroups and a homomorphism from a concrete semigroup, and determine minimal nonpure varieties. Next we characterize the cryptic ones in terms of their group elements and also by a homomorphism of a semigroup constructed in the paper. We also characterize groups and Clifford semigroups in a similar way by means of divisors. The paper also contains characterizations of completely semisimple inverse and of combinatorial inverse semigroups in a similar manner. It ends with a description of minimal non-$\mathcal {V}$ varieties, for varieties $\mathcal {V}$ of inverse semigroups considered.
The larval period in fishes has several definitions, each one deviating slightly from the other. Small discrepancies in the definitions, especially concerning the end of the larval period, can create misunderstandings when applied in practice. I examine the different definitions of a larva, the larval period, including metamorphosis, and the juvenile period. Various criteria used to identify the transition from the larval to juvenile periods are contradictory and refer mostly to the length of the larval period. Ignorance of definitions used to identify the juvenile period has caused many larvae to be regarded as juveniles. I discuss the feasibility of various definitions and the nomenclature on the basis of character evaluation. The occurrence of larval morphological characters, i.e. larval fin fold, differentiation of fins, temporary organs, absence of scale cover, non-adult like body proportions and pigmentation, is examined and some features are compared in eleven species. Irrespective of the different definitions of a larva, there are considerable differences in the schedule and duration of development in certain characters between species and, in terms of duration, also within species owing to environmental conditions. Ontogenetic processes seem to be sufficiently flexible to allow larvae to adapt to their environment, which on the other hand may also shape the phenotype. Determination of the environment in which a larva develops depends not only on the location of the spawning grounds but also on the dispersion of larvae. Dispersal strategies are examined in light of larval morphology and behaviour. After fin differentiation, the transition from larva to juvenile would seem to be best described by the dominant morphological changes in body proportions and coloration, combined with behavioural aspects and habitat changes. I suggest the differences and functional aspects of larvae be examined. The main character of larvae is that they are adapted to make use of resources not normally used by adults.