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Bifurcations in symplectic space

G. Ishikawa, S. Janeczko (2008)

Banach Center Publications

In this paper we take new steps in the theory of symplectic and isotropic bifurcations, by solving the classification problem under a natural equivalence in several typical cases. Moreover we define the notion of coisotropic varieties and formulate also the coisotropic bifurcation problem. We consider several symplectic invariants of isotropic and coisotropic varieties, providing illustrative examples in the simplest non-trivial cases.

Cohen-Macaulayness of multiplication rings and modules

R. Naghipour, H. Zakeri, N. Zamani (2003)

Colloquium Mathematicae

Let R be a commutative multiplication ring and let N be a non-zero finitely generated multiplication R-module. We characterize certain prime submodules of N. Also, we show that N is Cohen-Macaulay whenever R is Noetherian.

Deforming syzygies of liftable modules and generalised Knörrer functors

Runar Ile (2007)

Collectanea Mathematica

Maps between deformation functors of modules are given which generalise the maps induced by the Knörrer functors. These maps become isomorphisms after introducing certain equations in the target functor restricting the Zariski tangent space. Explicit examples are given on how the isomorphisms extend results about deformation theory and classification of MCM modules to higher dimensions.

(Generalized) filter properties of the amalgamated algebra

Yusof Azimi (2022)

Archivum Mathematicum

Let R and S be commutative rings with unity, f : R S a ring homomorphism and J an ideal of S . Then the subring R f J : = { ( a , f ( a ) + j ) a R and j J } of R × S is called the amalgamation of R with S along J with respect to f . In this paper, we determine when R f J is a (generalized) filter ring.

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