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- Title
The identity problem of finitely generated bi-ideals.
- Authors
Lorencs, A.
- Abstract
Finitely generated bi-ideals with letters from a selected alphabet A are considered. We solve the equivalence problem for generating systems of bi-ideals, i.e., look for an effective procedure which provides the means of determining if two generating systems $${\langle u_0, . . . , u_{m-1} \rangle}$$ and $${\langle v_0, . . . , v_{n-1} \rangle}$$ represent equal or different bi-ideals. We offer a method of constructing, for every generating system $${\langle u_0, . . . , u_{m-1} \rangle}$$ , an equivalent generating system $${\langle u^{\prime}_{0}, . . . , u^{\prime}_{m-1} \rangle}$$ with differing members. We also describe an algorithm for deciding if two generating systems $${\langle u_0, u_1 \rangle}$$ and $${\langle v_0, v_1 \rangle}$$ are equivalent or not. For a general case, the problem of existence of such an algorithm remains open.
- Subjects
GENERATORS of ideals (Algebra); MATHEMATICAL analysis; ALGORITHMS; PROBLEM solving; ALGEBRAIC fields; SEMIGROUPS (Algebra)
- Publication
Acta Informatica, 2012, Vol 49, Issue 2, p105
- ISSN
0001-5903
- Publication type
Article
- DOI
10.1007/s00236-012-0152-4