The concepts of an annihilator and a relative annihilator in an autometrized $l$-algebra are introduced. It is shown that every relative annihilator in a normal autometrized $l$-algebra $\mathcal {A}$ is an ideal of $\mathcal {A}$ and every principal ideal of $\mathcal {A}$ is an annihilator of $\mathcal {A}$. The set of all annihilators of $\mathcal {A}$ forms a complete lattice. The concept of an $I$-polar is introduced for every ideal $I$ of $\mathcal {A}$. The set of all $I$-polars is a complete lattice which becomes a two-element chain provided $I$ is prime. The $I$-polars are characterized as pseudocomplements in the lattice of all ideals of $\mathcal {A}$ containing $I$.
Climate features that influence life cycles, notably severity, seasonality, unpredictability and variability, are summarized for different polar zones. The zones differ widely in these factors and how they are combined. For example, seasonality is markedly reduced by oceanic influences in the Subantarctic. Information about the life cycles of Arctic and Antarctic arthropods is reviewed to assess the relative contributions of flexibility and programming to life cycles in polar regions. A wide range of life cycles occurs in polar arthropods and, when whole life cycles are considered, fixed or programmed elements are well represented, in contrast to some recent opinions that emphasize the prevalence of flexible or opportunistic responses. Programmed responses ale especially common for controlling the appearance of stages that are sensitive to adverse conditions, such as the reproductive adult. The relative contribution of flexibility and programming to different life cycles is correlated with taxonomic affinity (which establishes the general lifecycle framework for a species), and with climatic zone, the habitats of immature and adult stages, and food., Hugh V. Danks, and Lit
In this paper we deal with a pseudo effect algebra $\Cal A$ possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein, $\Cal A$ can be represented as an interval of a unital partially ordered group $G$. We prove that $\Cal A$ is projectable (strongly projectable) if and only if $G$ is projectable (strongly projectable). An analogous result concerning weak homogeneity of $\Cal A$ and of $G$ is shown to be valid.
It is shown that pseudo BL-algebras are categorically equivalent to certain bounded DRl-monoids. Using this result, we obtain some properties of pseudo BL-algebras, in particular, we can characterize congruence kernels by means of normal filters. Further, we deal with representable pseudo BL-algebras and, in conclusion, we prove that they form a variety.