In the study of pre-Lie algebras, concept pre-morphism arises naturally as a generalization standard notion morphism. Pre-morphisms can be defined for arbitrary (not-necessarily associative) algebras over any commutative ring k with identity, and dualized in various ways to generalized morphisms (related pre-Jordan algebras) anti-pre-morphisms anti-pre-Lie algebras). We consider idempotent pre-...

We define two resource aware typing systems for the λμ-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial arguments –based on decreasing measures of type derivations– to characterize head and strongly normalizing terms. Moreover, typability provides upper bounds for the length of head-reduction sequences and maximal redu...

Abstract In this paper, we exhibit that, in an incline L, the greatest element ‘1’ is the multiplicative identity for the elements of DL, the set of idempotent elements in L. We have discussed the invertibility of matrices over DL and for matrices over an integral incline. We have obtained equivalent conditions for regularity of a matrix over an incline whose idempotent elements are linearly or...

In [15], Kaplansky introduced Baer rings as rings in which every right (left) annihilator ideal is generated by an idempotent. According to Clark [9], a ring R is called quasi-Baer if the right annihilator of every right ideal is generated (as a right ideal) by an idempotent. Further works on quasi-Baer rings appear in [4, 6, 17]. Recently, Birkenmeier et al. [8] called a ring R to be a right (...

For an arbitrary left Artinian ring R, explicit descriptions are given of all the left denominator sets S of R and left localizations SR of R. It is proved that, up to R-isomorphism, there are only finitely many left localizations and each of them is an idempotent localization, i.e. SR ≃ S e R and ass(S) = ass(Se) where Se = {1, e} is a left denominator set of R and e is an idempotent. Moreover...

Termination analysis is often performed over the abstract domains of monotonicity constraints or of size change graphs. First, the transition relation for a given program is approximated by a set of descriptions. Then, this set is closed under a composition operation. Finally, termination is determined if all of the idempotent loop descriptions in this closure have (possibly different) ranking ...

A finite-dimensional commutative algebra A over a field K is called a Bernstein algebra if there exists a non-trivial homomorphism co: A -> K (baric algebra) such that the identity (x) = CO(X)JC holds in A (see [7]). The origin of Bernstein algebras lies in genetics (see [2,8]). Holgate (in [2]) was the first to translate the problem into the language of non-associative algebras. Information ab...

When conjunctively merging two belief functions concerning a single variable but coming from different sources, Dempster rule of combination is justified only when information sources can be considered as independent. When dependencies between sources are ill-known, it is usual to require the property of idempotence for the merging of belief functions, as this property captures the possible red...

A very brief introduction to tropical and idempotent mathematics is presented. Tropical mathematics can be treated as a result of a dequantization of the traditional mathematics as the Planck constant tends to zero taking imaginary values. In the framework of idempotent mathematics usually constructions and algorithms are more simple with respect to their traditional analogs. We especially exam...

In this paper, we present an algebraic approach to idempotent functional analysis, which is an abstract version of idempotent analysis in the sense of [1–3]. Elements of such an approach were used, for example, in [1, 4]. The basic concepts and results are expressed in purely algebraic terms. We consider idempotent versions of certain basic results of linear functional analysis , including the ...