Modular and lower-modular elements of lattices of semigroup varieties

The paper contains three main results. First, we show that if a commutative semigroup variety is a modular element of the lattice Com of all commutative semigroup varieties then it is either the variety COM of all commutative semigroups or a nil-variety or the join of a nil-variety with the variety of semilattices. Second, we prove that if a commutative nil-variety is a modular element of Com then it may be given within COM by 0-reduced and substitutive identities only. Third, we completely classify all lower-modular elements of Com. As a corollary, we prove that an element of Com is modular whenever it is lower-modular. All these results are precise analogues of results concerning modular and lower-modular elements of the lattice of all semigroup varieties obtained earlier by Jezek, McKenzie, Vernikov, and the author. As an application of a technique developed in this paper, we provide new proofs of the `prototypes' of the first and the third our results.Comment: 15 page

Generalized Green'S Equivalences on the Subsemigroups of the Bicyclic Monoid

We study generalized Green's equivalences on all subsemigroups of the bicyclic monoid B and determine the abundant (and adequate) subsemigroups of B. © 2010 Copyright Taylor and Francis Group, LLC

The Ekaterinburg Seminar "Algebraic Systems": 50 Years of Activities

The aim of the present article is to give a characterization of distinctive features of the scientic seminar founded and led by the author as well as to show the main sides of its activities during half a century

SOME ABSTRACT PROPERTIES OF SEMIGROUPS APPEARING IN SUPERCONFORMAL THEORIES

A new type of semigroups which appears while dealing with $N=1$ superconformal symmetry in superstring theories is considered. The ideal series having unusual abstract properties is constructed. Various idealisers are introduced and studied. The ideal quasicharacter is defined. Green's relations are found and their connection with the ideal quasicharacter is established.Comment: 11 page

Bone invading NSCLC cells produce IL-7: mice model and human histologic data

<p>Abstract</p> <p>Background</p> <p>Bone metastases are a common and dismal consequence of lung cancer that is a leading cause of death. The role of IL-7 in promoting bone metastases has been previously investigated in NSCLC, but many aspects remain to be disclosed. To further study IL-7 function in bone metastasis, we developed a human-in-mice model of bone aggression by NSCLC and analyzed human bone metastasis biopsies.</p> <p>Methods</p> <p>We used NOD/SCID mice implanted with human bone. After bone engraftment, two groups of mice were injected subcutaneously with A549, a human NSCLC cell line, either close or at the contralateral flank to the human bone implant, while a third control group did not receive cancer cells. Tumor and bone vitality and IL-7 expression were assessed in implanted bone, affected or not by A549. Serum IL-7 levels were evaluated by ELISA. IL-7 immunohistochemistry was performed on 10 human bone NSCLC metastasis biopsies for comparison.</p> <p>Results</p> <p>At 12 weeks after bone implant, we observed osteogenic activity and neovascularization, confirming bone vitality. Tumor aggressive cells implanted close to human bone invaded the bone tissue. The bone-aggressive cancer cells were positive for IL-7 staining both in the mice model and in human biopsies. Higher IL-7 serum levels were found in mice injected with A549 cells close to the bone implant compared to mice injected with A549 cells in the flank opposite to the bone implant.</p> <p>Conclusions</p> <p>We demonstrated that bone-invading cells express and produce IL-7, which is known to promote osteoclast activation and osteolytic lesions. Tumor-bone interaction increases IL-7 production, with an increase in IL-7 serum levels. The presented mice model of bone invasion by contiguous tumor is suitable to study bone-tumor cell interaction. IL-7 plays a role in the first steps of metastatic process.</p

Semigroups with certain finiteness conditions and Chernikov groups

The main purpose of this short survey is to show how groups of special structure, which are accepted to be called Chernikov groups, appeared in the considerations of semigroups with certain finiteness conditions. A structure of groups with several such conditions has been described (they turned out to be special types of Chernikov groups). Lastly, a question concerning some special type of Chernikov groups is recalled; this question was raised by the author more than 35 years ago, and it is still open. © Journal "Algebra and Discrete Mathematics"

A Word about Petr Grigor’evich Kontorovich

100-летие со дня рождения Петра Григорьевича Конторовича мы отмечаем в 2005 году. Петр Григорьевич принадлежит к числу ученых, с чьими именами связано становление Уральского университета

First years of the Sverdlovsk algebraic school

Статья является слегка модифицированной версией статьи, опубликованной в №16 «Известий Уральского государственного университета» (2000), адресованном широкому кругу читателей