Computing the structure of a finite-dimensional algebra is a classical mathematical problem in symbolic computation with many applications such as polynomial factorization, computational group theory and differential factorization. We will investigate the computational complexity and exhibit new algorithms for this problem over the field Fq(y), where Fq is the finite field with q elements. A fi...

In this paper, we give the explicit structure of $ \otimes^{3} H and \wedge^{3} where is a generalized Heisenberg Lie algebra rank at most 2. Moreover, for non-abelian nilpotent L, obtain an upper bound dimension L.

In [Ban97] a connection among rough sets (in particular, pre-rough algebras) and three-valued Łukasiewicz logic Ł3 is pointed out. In this paper we present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95, EG01]), in which the logic of every instant is given by Ł3: a completeness theorem will be shown. This is the prosecution of the work initiated in [AGM08] and [ABM09], in whic...

It is known that the dimension of Schur multiplier a non-abelian nilpotent Lie algebra L n equal to 1 2 (n − 1)(n 2) + s(L) for some ≥ 0. The structure all algebras has been given ≤ 4 in several

In this paper, Jordan–Kronecker invariants are calculated for all nilpotent 6- and 7-dimensional Lie algebras. We consider the Poisson bracket family, depending on lambda parameter a coalgebra, i.e., linear space dual to algebra. For some

The structure theory for Pi-algebras is well developed. Some results of this theory are classic now. One of them is Kaplansky's theorem which asserts that a primitive Pi-algebra is finite dimensional over its centre. Another example is the theorem of Nagata-Higman which asserts that any algebra over a field of zero characteristic satisfying identity x" = 0 is nilpotent. In 1957 A.I. Shirshov pr...

It is known that a right nilpotent congruence on a-nite algebra A is also left nilpotent Kea93]. The question on whether the left nilpotency class of is less than or equal to the right nilpo-tency class of is still open. In this paper we nd an upper limit for the left nilpotency class of. In addition, under the assumption that 1 6 2 typ fAg, we show that (] k =) k for all k 1. Thus the left and...

An improvement of a bound of Yankosky (2003) is presented in this paper, thanks to a restriction which has been recently obtained by the authors on the Schur multiplier M(L) of a finite dimensional nilpotent Lie algebra L. It is also described the structure of all nilpotent Lie algebras such that the bound is attained. An important role is played by the presence of a derived subalgebra of maxim...

Let G be a complex simple algebraic group and let g be its Lie algebra. A nilpotent orbit O in g is an orbit of a nilpotent element of g by the adjoint action of G on g. Then O admits a natural symplectic 2-form ω and the nilpotent orbit closure Ō has symplectic singularities in the sense of [Be] and [Na3] (cf. [Pa], [Hi]). In [Ri], Richardson introduced the notion of so-called the Richadson or...

In this paper we study generic expansions of predicate logics of some left-continuous t-norms (mainly Gödel and Nilpotent Minimum predicate logics) with a countable set of truth-constants. Using known results on tnorm based predicate fuzzy logics we obtain results on the conservativeness and completeness for the expansions of some predicate fuzzy logics. We describe the problem for the cases of...