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Discussiones Mathematicae - General Algebra and Applications

2008 | 28 | 2 | 193-208
Tytuł artykułu

On the lattice of congruences on inverse semirings

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let S be a semiring whose additive reduct (S,+) is an inverse semigroup. The relations θ and k, induced by tr and ker (resp.), are congruences on the lattice C(S) of all congruences on S. For ρ ∈ C(S), we have introduced four congruences $ρ_{min}, ρ_{max}, ρ^{min}$ and $ρ^{max}$ on S and showed that $ρθ = [ρ_{min},ρ_{max}]$ and $ρκ = [ρ^{min},ρ^{max}]$. Different properties of ρθ and ρκ have been considered here. A congruence ρ on S is a Clifford congruence if and only if $ρ_{max}$ is a distributive lattice congruence and $ρ^{max}$ is a skew-ring congruence on S. If η (σ) is the least distributive lattice (resp. skew-ring) congruence on S then η ∩ σ is the least Clifford congruence on S.
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
193-208
Opis fizyczny
Daty
wydano
2008
otrzymano
2008-01-07
poprawiono
2008-03-20
Twórcy
autor
• Illambazar B.K. Roy Smiriti Balika Vidyalaya Illambazar, Birbhum, West Bengal, India
autor
• Department of Mathematics, Visva-Bharati University, Santiniketan - 731235, West Bengal, India
Bibliografia
• [1] R. Feigenbaum, Kernels of orthodox semigroup homomorphisms, J. Austral. Math. Soc. 22 (A) (1976), 234-245.
• [2] R. Feigenbaum, Regular semigroup congruences, Semigroup Forum 17 (4) (1979), 373-377.
• [3] D.G. Green, The lattice of congruences on an inverse semigroup, Pacific J. Math. 57 (1975), 141-152.
• [4] M.P. Grillet, Semirings with a completely simple additive Semigroup, J. Austral. Math. Soc. 20 (A) (1975), 257-267.
• [5] J.M. Howie, Fundamentals of Semigroup Theory, Clarendon Press, Oxford 1995.
• [6] S.K. Maity, Congruences on additive inverse semirings, Southeast Asian Bull. Math. 30 (2006).
• [7] F. Pastijn and M. Petrich, Congruences on regular semigroups, Trans. Amer. Math. Soc. 295 (2) (1986), 607-633.
• [8] M. Petrich, Congruences on Inverse Semigroups, Journal of Algebra 55 (1978), 231-256.
• [9] M. Petrich, Inverse Semigroups, John Wiley & Sons 1984.
• [0] M. Petrich and N.R. Reilly, A network of congruences on an inverse semigroup, Trans. Amer. Math. Soc. 270 (1) (1982), 309-325.
• [1] N.R. Reilly and H.E. Scheiblich, Congruences on regular semigroups, Pacific J. Math. 23 (1967), 349-360.
• [2] H.E. Scheiblich, Kernels of inverse semigroup homomorphisms, J. Austral. Math. Soc. 18 (1974), 289-292.
• [3] M.K. Sen, S. Ghosh and P. Mukhopadhyay, Congruences on inverse semirings, pp. 391-400 in: Algebras and Combinatorics (Hong Kong, 1997), Springer, Singapore 1999.
• [4] M.K. Sen, S.K. Maity and K.P. Shum, On completely regular semirings, Bull. Cal. Math. Soc. 98 (4) (2006), 319-328.
• [5] M.K. Sen, S.K. Maity and K.P. Shum, Clifford semirings and generalized Clifford semirings, Taiwanese Journal of Mathematics 9 (3) (2005), 433-444.
Typ dokumentu
Bibliografia
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