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This article is cited in 1 scientific paper (total in 1 paper)
On the compressive radical of semigroups
E. N. Roiz
Abstract:
A centered right $S$-polygon (synonyms: $S$-operand, $S$-system) $A$ is called right compressive if $AS\ne0$ and $\alpha a=\alpha b\to\alpha=0\vee(a,b)\in(\operatorname{Ker}A)_S$ and leftt compressive if $AS\ne0$ and $\alpha a=\beta a\to\alpha=\beta\vee Aa=0$. Here $(\operatorname{Ker}A)_S$ is the congruence on the semigroup $S$ called the kernel of the $S$-polygon $A$ which is defined as follows: $(a,b)\in(\operatorname{Ker}A)_S\leftrightarrow(\forall\,\alpha\in A)(\alpha a=\alpha b)$.
The intersection of the kernels of all right (left) compressive $S$-polygons is called the right (left) compressive radical of $S$. In this paper we study compressively semisimple and compressively radical semigroups.
Bibliography: 11 titles.
Received: 23.10.1972
Citation:
E. N. Roiz, “On the compressive radical of semigroups”, Mat. Sb. (N.S.), 92(134):4(12) (1973), 530–540; Math. USSR-Sb., 21:4 (1973), 523–534
Linking options:
https://www.mathnet.ru/eng/sm3428https://doi.org/10.1070/SM1973v021n04ABEH002033 https://www.mathnet.ru/eng/sm/v134/i4/p530
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Abstract page: | 238 | Russian version PDF: | 82 | English version PDF: | 3 | References: | 38 |
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