1,721,245 research outputs found
Towards a classification of maximal unicellular bands
No full textPT: J; CR: HOFFMAN K, 1971, LINEAR ALGEBRA RADJAVI H, 1985, J OPERAT THEOR, V13, P65; NR: 2; TC: 12; J9: SEMIGROUP FORUM; PG: 21; GA: NX937Source type: Electronic(1
Matrix semigroups with commutable rank
No full textWe focus on matrix semigroups (and algebras) on which rank is commutable [rank(AB) = rank(BA)]. It is shown that in a number of cases (for example, in dimensions less than 6), but not always, commutativity of rank entails permutability of rank [rank(A(1)A(2)...A(n)) = rank(A(sigma(1))A(sigma(2))... A(sigma(n)))]. It is shown that a commutable-rank semigroup has a natural decomposition as a semi-lattice of semigroups that have a simpler structure. While it is still unknown whether commutativity of rank entails permutability of rank for algebras, the question is reduced to the case of algebras of nilpotents.PT: J; CR: ANDERSON FW, 1992, GRADUATE TEXTS MATH ANDO T, 1987, LINEAR ALGEBRA APPL, V90, P165 GANTMACHER FR, 1937, COMPOS MATH, P445 HORN RA, 1990, MATRIX ANAL LEVITZKI J, 1931, MATH ANN, V105, P620 LIVSHITS L, 1998, J OPERAT THEOR, V40, P35 OKNINSKI J, 1998, SERIES ALGEBRA, V6 PRASOLOV VV, 1994, PROBLEMS THEOREMS LI RADJAVI H, 2000, SIMULTANEOUS TRIANGU WHITNEY AM, 1952, J ANAL MATH, V2, P88; NR: 10; TC: 1; J9: SEMIGROUP FORUM; PG: 29; GA: 698NQSource type: Electronic(1
Green index in semigroups : generators, presentations and automatic structures
No full textThe Green index of a subsemigroup T of a semigroup S is given by counting strong orbits in the complement S n T under the natural actions of T on S via right and left multiplication. This partitions the complement S nT into T-relative H -classes, in the sense of Wallace, and with each such class there is a naturally associated group called the relative Schützenberger group. If the Rees index ΙS n TΙ is finite, T also has finite Green index in S. If S is a group and T a subgroup then T has finite Green index in S if and only if it has finite group index in S. Thus Green index provides a common generalisation of Rees index and group index. We prove a rewriting theorem which shows how generating sets for S may be used to obtain generating sets for T and the Schützenberger groups, and vice versa. We also give a method for constructing a presentation for S from given presentations of T and the Schützenberger groups. These results are then used to show that several important properties are preserved when passing to finite Green index subsemigroups or extensions, including: finite generation, solubility of the word problem, growth type, automaticity (for subsemigroups), finite presentability (for extensions) and finite Malcev presentability (in the case of group-embeddable semigroups).Peer reviewe
On Numerical Semigroups Related To Covering Of Curves
No full textWe investigate arithmetical properties of a class of semigroups that includes those appearing as Weierstrass semigroups at totally ramified points of covering of curves.673344354Accola, R.D.M., On Castelnuovo's inequality for algebraic curves, I (1979) Trans. Amer. Math. Soc., 251, pp. 357-373Arbarello, E., Cornalba, M., Griffiths, P.A., Harris, J., (1985) Geometry of Algebraic Curves, 1. , Springer-VerlagCastelnuovo, G., Ricerche di geometria sulle curve algebriche (1889) Atti. R. Acad. Sci. Torino, 24, pp. 196-223Eisenbud, D., Harris, J., Existence, decomposition, and limits of certain Weierstrass points (1987) Invent. Math., 87, pp. 495-515Farkas, H.M., Kra, I., Riemann surfaces (1992) Grad. Texts in Math., 71. , (second edition) Springer-Verlag, New York/BerlinFreiman, G.A., Foundation of a structural theory of set addition (1973) Transl. Math. Monogr., 37. , Amer. Math. Soc., Providence, RIGarcia, A., Weights of Weierstrass points in double coverings of curves of genus one or two (1986) Manuscripta Math., 55, pp. 419-432Hartshorne, R., Algebraic geometry (1977) Grad. Texts in Math., 52. , Springer-Verlag, New York/BerlinHomma, M., On Esteves's inequality of order sequences of curves (1993) Comm. Algebra, 21 (10), pp. 3685-3689Kato, T., On the order of a zero of the theta function (1977) Kodai Math. Sem. Rep., 28, pp. 390-407Kato, T., Non-hyperelliptic Weierstrass points of maximal weights (1979) Math. Ann., 239, pp. 141-147Kato, T., On criteria of g̃-hyperellipticity (1979) Kodai Math. J., 2, pp. 275-285Komeda, J., Non-Weierstrass numerical semigroups (1998) Semigroup Forum, 57 (2), pp. 157-185Nijenhuis, A., Wilf, H.S., Representations of integers by linear forms in nonnegative integers (1972) J. Number Theory, 4, pp. 98-106Oliveira, G., Weierstrass semigroups and the canonical ideal of non-trigonal curves (1991) Manuscripta Math., 71, pp. 431-450Rathmann, J., The uniform position principle for curves in characteristic p (1987) Math. Ann., 276, pp. 565-579Selmer, E.S., On the linear diophantine problem of Frobenius (1977) J. Reine Angew. Math., 293-294, pp. 1-17Torres, F., Weierstrass points and double coverings of curves with applications: Symmetric numerical semigroups which cannot be realized as Weierstrass semigroups (1994) Manuscripta Math., 83, pp. 39-58Torres, F., On certain N-sheeted coverings of curves and numerical semigroups which cannot be realized as Weierstrass semigroups (1995) Comm. Algebra, 23 (11), pp. 4211-4228Torres, F., On γ-hyperelliptic numerical semigroups (1997) Semigroup Forum, 55, pp. 364-379Torres, F., On the constellations of Weierstrass points (1997) Arch. Math., 68 (2), pp. 139-14
Topological properties of inverse limits of free abelian monoids, with an application to inverse limits of UFDs, Semigroup Forum (vol 59, pg 418, 1999)
No full textCovers for S-acts and condition (A) for a monoid S
Full text linkA monoid S satisfies Condition (A) if every locally cyclic left S-act is cyclic. This condition first arose in Isbell’s work on left perfect monoids, that is, monoids such that every left S-act has a projective cover. Isbell showed that S is left perfect if and only if every cyclic left S-act has a projective cover and Condition (A) holds. Fountain built on Isbell’s work to show that S is left perfect if and only if it satisfies Condition (A) together with the descending chain condition on principal right ideals, MR. We note that a ring is left perfect (with an analogous definition) if and only if it satisfies MR. The appearance of Condition (A) in this context is therefore monoid specific.Condition (A) has a number of alternative characterisations, in particular, it is equivalent to the ascending chain condition on cyclic subacts of any left S-act. In spite of this, it remains somewhat esoteric. The first aim of this article is to investigate the preservation of Condition (A) under basic semigroup-theoretic constructions.Recently, Khosravi, Ershad and Sedaghatjoo have shown that every left S-act has a strongly flat or Condition (P) cover if and only if every cyclic left S-act has such a cover and Condition (A) holds. Here we find a range of classes of S-acts C such that every left S-act has a cover from C if and only if every cyclic left S-act does and Condition (A) holds. In doing so we find a further characterisation of Condition (A) purely in terms of the existence of covers of a certain kind.Finally, we make some observations concerning left perfect monoids and investigate a class of monoids close to being left perfect, which we name left IPa-perfect
Partial maps with domain and range: extending Schein's representation
No full textThe semigroup of all partial maps on a set under the operation of composition admits a number of operations relating to the domain and range of a partial map. Of particular interest are the operations R and L returning the identity on the domain of a map and on the range of a map respectively. Schein [25] gave an axiomatic characterisation of the semigroups with R and L representable as systems of partial maps; the class is a finitely axiomatisable quasivariety closely related to ample semigroups (which were introduced—as type A semigroups—by Fountain, [7]). We provide an account of Schein's result (which until now appears only in Russian) and extend Schein's method to include the binary operations of intersection, of greatest common range restriction, and some unary operations relating to the set of fixed points of a partial map. Unlike the case of semigroups with R and L, a number of the possibilities can be equationally axiomatised
Smarandache U-liberal semigroup structure
Full text linkIn this paper, Smarandache U-liberal semigroup structure is given. It is shown that
a semigroup S is Smarandache U-liberal semigroup if and only if it is a strong semilattice of some rectangular monoids. Consequently, some corresponding results on normal orthocryptous semigroups and normal orthocryptogroups are generalized and extended
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