Results 1 to 10 of about 1,243,990 (68)
Biordered sets come from semigroups [PDF]
Journal of Algebra, 1985 The biordered set of a semigroup is the set of idempotents of the semigroup together with the partial operation obtained by restriction of the multiplication to those pairs of idempotents whose product is equal to one of them (i.e. one is a one-sided zero of the other).
Easdown, D
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PERIODIC ELEMENTS OF THE FREE IDEMPOTENT GENERATED SEMIGROUP ON A BIORDERED SET [PDF]
International Journal of Algebra and Computation, 2010 We show that every periodic element of the free idempotent generated semigroup on an arbitrary biordered set belongs to a subgroup of the semigroup.
David Easdown +2 more
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Semigroup Forum, 1984 \textit{K. S. S. Nambooripad} [Mem. Am. Math. Soc. 224 (1979; Zbl 0457.20051)] introduced the concept of a (regular) biordered set to abstractly characterize the set of idempotents of a regular semigroup. He also described the biordered sets associated with bands.
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Reconstructing some idempotent-generated semigroups from their biordered sets
Semigroup Forum, 1984 The authors investigate how many informations on a semigroup \(S\) are given by the partial algebra \(E(S)\) of the idempotents of \(S\) where a product of \((e,f)\) is defined iff, under the multiplication of \(S\), \(ef\) or \(fe\) is equal to one of its factors. \(E(S)\) is the biordered set of \(S\).
T E Hall
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A concept of variety for regular biordered sets
Semigroup Forum, 1994 A regular biordered set \((E,\cdot,\omega^ l, \omega^ r)\) is a set \(E\) together with two quasiorders \(\omega^ l\) and \(\omega^ r\) and a partial binary operation \(\cdot\), satisfying a finite (but somehow complicated) system of axioms. Regular biordered sets were introduced by \textit{K. S. S. Nambooripad} [Mem. Am. Math. Soc. 224 (1979; Zbl 0457.
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Independence of axioms for biordered sets
Semigroup Forum, 1984 Biordered sets were introduced by \textit{K. S. S. Nambooripad} as an abstraction of the partial semigroup of idempotents of a semigroup [Mem. Am. Math. Soc. 224 (1979; Zbl 0457.20051]. Let X, Y be sets, \(\rho \subseteq X\times Y\) and put \(\rho(y)=\{x\in X:\quad x\rho y\}.\) A partial algebra is defined to be a set E equipped with a partial binary ...
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Biordered sets and complemented modular lattices
Semigroup Forum, 1980 In this paper we give a structure theorem for the biordered set of a strongly regular Baer semigroup. As a result we shall be able to construct the biordered set of the multiplicative semigroup of a regular ring in terms of the complemented modular lattice which is coordinatized by this regular ring.
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ℓ2$\ell ^2$‐Betti numbers and coherence of random groups
Journal of the London Mathematical Society, Volume 106, Issue 1, Page 425-445, July 2022., 2022 Abstract We study ℓ2$\ell ^2$‐Betti numbers, coherence and (virtual) fibring of random groups in the few‐relator model. In particular, random groups with negative Euler characteristic are coherent, have ℓ2$\ell ^2$‐homology concentrated in dimension 1 and embed in a virtually free‐by‐cyclic group with high probability.
Dawid Kielak +2 more
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Relations between cross-connections and biordered sets
Semigroup Forum, 1978 K S S Nambooripad
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Biordered sets are biordered subsets of idempotents of semigroups [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1984 AbstractA new arrow notation is used to describe biordered sets. Biordered sets are characterized as biordered subsets of the partial algebras formed by the idempotents of semigroups. Thus it can be shown that in the free semigroup on a biordered set factored out by the equations of the biordered set there is no collapse of idempotents and no new ...
openaire +2 more sources