The notion of initial ideal for an a polynomial ring appears in the theory Gröbner basis. Similarly to ideals, we can define algebra subalgebra ring, or more generally Laurent which is used SAGBI (Subalgebra Analogue Bases Ideals) finitely generated not always generated, and no general criterion finite generation known. aim this paper present new class subalgebras having non-finitely algebras. ...

In this paper, the authors extend concept of a t-intuitionistic fuzzy set to PMS-subalgebras PMS-algebras. The define PMS-subalgebra PMS-algebra and show that any intuitionistic is PMS-subalgebra. provide condition for an in be use their (α,β) level cuts characterize PMS-algebra. investigate whether homomorphic images inverse are also PMS-subalgebras. Furthermore, nonempty again Finally, Cartes...

In this paper, we begin to study the subalgebra lattice of a Leibniz algebra. particular, deal with algebras whose is modular, upper semi-modular, lower distributive, or dually atomistic. The fact that non-Lie algebra has fewer one-dimensional subalgebras in general results number conditions being weaker than Lie case.

A Poisson geometry arising from maximal commutative subalgebras is studied. A spectral sequence convergent to Hochschild homology with coefficients in a bimodule is presented. It depends on the choice of a maximal commutative subalgebra inducing appropriate filtrations. Its E p,q -groups are computed in terms of canonical homology with values in a Poisson module defined by a given bimodule and ...