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Some structure to be completely regular semiring congruence

Author: SunYongLi
Tutor: LiShiZheng；ZhangYuFen
School: Shandong Normal University
Course: Basic mathematics
Keywords: Completely regular semigroups Completely regular semiring To be completely regular semiring Congruence
CLC: O153.3
Type: Master's thesis
Year: 2000
Downloads: 31
Quote: 0
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Abstract


This paper studies some structure to be completely regular semiring congruence. In the second quarter, the first reference [1] in Mario Petrich (1987) given completely regular semigroups a structure theorem Secondly completely regular semiring (S,, ·) in E ] = E [·] (S,, ·) structure and E when certain conditions are met, the following conclusions: the theorem in the second half of the ring (S, ·) , E [] = E [·] , S is completely regular semi-ring if and only if S is completely simple semi-ring - semilattice semiring. Theorem Let (S,, ·) for the half-ring and E [] = E [·] , S is completely regular semiring and E with a half-ring if and only if, where E is the rectangle with the half ring E α distributive lattice Y, G group semirings G α distributive lattice Y, where X Y spined product. In the third quarter, by [4] in, Stojan Bodanovic for some quasi completely regular semigroup description of the structure, gives the corresponding intends to completely regular semiring structure, the main conclusions are as follows: Theorem Let semi-ring (S , ·) in E [] = E [·] S is intended to completely inverse half-ring, and for (?) e, f ∈ E the following equation holds : e ef e = e, ef fe ef = ef. S is the half-ring quasigroups distributive lattices. Theorem Let (S,, ·) The semiring E [] = E [·] , the (S, ·) is intended to completely inverse half-ring, and The E grid when assigned and only if S is quasigroups semirings distributive lattices, while E [] subsemigroup. Theorem Let (S,, ·) semi-ring meet E [] = E [·] , S is a quasi completely inverse semi-ring if and only if S is a quasi group semi-ring - semilattice semiring. Theorem Let (S,, ·) for the half-ring meet E [] = E [] (S,, ·) is intended to completely regular semi-ring and E with a half-ring if and only if S is completely Archimedean semirings distributive lattices, and E [] subsemigroup. meet points \] Howte to some special semigroup minimum group congruence description Buchuan. Stojan Bodanovic intends to completely regular semigroups minimum group congruence characterization, given the corresponding quasi completely regular semiring minimum ring congruence. mainly the following conclusions: Theorem semirings u \\ * plus inverse semiring defined S relationship corpse as follows: n = Xa, b). S. The cited (3e. E) a + e = b + e} carcasses on S smallest ring with the remainder theorem plus contemplated inverse semi-ring S, \\ ·) on the relationship corpse follows the definition: p-= u mouth, DjE two Xbl (] eE on export) + e = 0 + X) corpse for the S smallest ring of congruence.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Abstract algebra ( Algebra ) > Ring Theory
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