6533b82efe1ef96bd12930be

RESEARCH PRODUCT

Partial Finitely Generated Bi-Ideals

Raivis BetsJanis Buls

subject

Discrete mathematicsStatement (computer science)Mathematics::Commutative Algebra020207 software engineering0102 computer and information sciences02 engineering and technologyBasis (universal algebra)01 natural sciencesElectronic mailSection (category theory)Stallings theorem about ends of groups010201 computation theory & mathematics0202 electrical engineering electronic engineering information engineeringFinitely-generated abelian groupFinite setCounterexampleMathematics

description

Partial words have been studied by Blanchet-Sadri et al., but bi-ideals or reccurrent words have been studied for centuries by many researchers. This paper gives a solution for some problems for partial reccurrent words. This paper gives an algorithm for a given finitely generated bi-ideal, how to construct a new basis of ultimately finitely generated bi-ideal, which generates the same given bi-ideal. The paper states that it is always possible to find a basis for a given finitely generated bi-ideal. The main results of this paper are presented in third section. At first, we show that if two irreduciable bi-ideals are different, they will differ in infinitely many places. This led to the statement that it is possible to fill the finite number of holes for a given finitely generated bi-ideal, but a counterexample shows that it is not possible for infinitely many holes.

yearjournalcountryeditionlanguage
2016-09-012016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)
https://doi.org/10.1109/synasc.2016.065