‎in this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  it shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. we investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. finally we extend krull's intersection theorem of fuzzy ideals by using concept $mu$-adic...

In this paper, some familiar and new results on arithmetical rings, modules, Bezout rings (not necessarily commutative) are provided. particular, we examine relationships between their localizations by maximal ideals, saturated submodules saturations, localizable properties of annihilators finitely generated modules over diagonalizable with flat right quasi-projective Hermite Pierce stalks, Kru...

A domain R is perinormal if every going-down overring flat and a globally localization of [2 Epstein, N., Shapiro, J. (2016). Perinormality - generalization Krull domains. Algebra 451:65–84. DOI: 10.1016/j.jalgebra.2015.12.002.[Crossref], [Web Science ®] , [Google Scholar]]. I show that global perinormality preserved in pullback construction which encompasses classical D + M construction. In do...

1212 Carlo Carbone , * Sandra Gardonio , Paolo Moras , Samir Lounis , Marcus Heide , Gustav Bihlmayer , Nicolae Atodiresei , Peter Heinz Dederichs , Stefan Blügel , Sergio Vlaic , Anne Lehnert , Safi a Ouazi , Stefano Rusponi , Harald Brune , Jan Honolka , Axel Enders , Klaus Kern , Sebastian Stepanow , Cornelius Krull , Timofey Balashov , Aitor Mugarza , and Pietro Gambardella Self-Assembled N...

In this paper, we use a characterization of R-modules N such that fdRN = pdRN to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting N to be the dth local cohomology functor of R with respect to the maximal ideal where d is the Krull dimension of R.

This is the fourth and last paper in a sequence on Krull dimension for limit groups, answering a question of Z. Sela. In it we finish the proof, analyzing limit groups obtained from other limit groups by adjoining roots. We generalize our work on Scott complexity and adjoining roots from the previous paper in the sequence to the category of limit groups.

For a finite dimensional monomial algebra Λ over a field K we show that the Hochschild cohomology ring of Λ modulo the ideal generated by homogeneous nilpotent elements is a commutative finitely generated Kalgebra of Krull dimension at most one. This was conjectured to be true for any finite dimensional algebra over a field in [13].

Study team: Paul Nathan [email protected] Rena Conti [email protected] Tara Henderson [email protected] Robin Yabroff [email protected] I-Chan Huang [email protected] Elyse Park [email protected] Kevin Krull [email protected] Anne Kirchhoff [email protected] Todd Gibson [email protected] Les Robison [email protected] Greg Armstrong g...

The proof of the following theorem is presented: If D is, respectively, a Krull domain, a Dedekind domain, or a PrGfer domain, then D is correspondingly a UFD, a PID, or a Bezout domain if and only if every irreducible quadratic polynomial in D[X] is a prime element.