ONE - SIDED k - IDEALS ANDh - IDEALS IN SEMIRINGSH
نویسنده
چکیده
ideals of these kinds; congruence class semirings. Abstract: Since they are closer related to the ring-theoretical concept of ideals than arbitrary semiring ideals, two-sided k-ideals and h-ideals occur in several statements on semirings. In this paper we investigate those ideals and also left-sided ones in arbitrary semirings S with commutative addition. For instance, we prove (for the rst time without any restrictions) that an ideal A of S is a maximal (left) k-ideal or h-ideal of S ii the congruence class semiring S== A of S determined by A has only two (trivial) ideals of this kind. Concerning other results we refer to a survey in the second part of the Introduction.
منابع مشابه
On Ideals Which Have the Weakly Insertion of Factors Property
A one-sided ideal of a ring has the insertion of factors property (or simply, IFP) if implies r for . We say a one-sided ideal of has the weakly IFP if for each , implies , for some non-negative integer . We give some examples of ideals which have the weakly IFP but have not the IFP. Connections between ideals of which have the IFP and related ideals of some ring extensions a...
متن کاملThe Semigroup of Ideals of a Fir Is
If R is a 2-sided fir (free ideal ring) with no non-trivial right invariant elements, we shall find that the non-zero 2-sided ideals of R, under the usual multiplication of ideals, form a free semigroup with 1. In particular, this holds when R is a free associative algebra over a field. (We also consider the operations of multiplying right ideals by 2-sided ideals to get right ideals, 2-sided i...
متن کاملIntra-regular Left Almost Semigroups Characterized by Their Anti Fuzzy Ideals
Abstract In this paper, we have introduced anti fuzzy quasi-ideals, anti fuzzy bi-(generalized bi-) ideals and anti fuzzy left (right, two-sided) ideals in LA-semigroup. Further we have characterized an intra-regular LA-semigroup by the properties of their anti fuzzy left (right, two-sided) ideals, anti fuzzy bi(generalized bi-)ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals. Fur...
متن کاملOn One-sided Lie Nilpotent Ideals of Associative Rings
We prove that a Lie nilpotent one-sided ideal of an associative ring R is contained in a Lie solvable two-sided ideal of R. An estimation of derived length of such Lie solvable ideal is obtained depending on the class of Lie nilpotency of the Lie nilpotent one-sided ideal of R. One-sided Lie nilpotent ideals contained in ideals generated by commutators of the form [. . . [[r1, r2], . . .], rn−1...
متن کامل