RM ALGEBRAS AND COMMUTATIVE MOONS
نویسندگان
چکیده
Some generalizations of BCI algebras (the RM, BH, CI, BCH,
 BH**, BCH**, and *aRM** algebras) satisfying the identity $(x \rightarrow
 1)\rightarrow y = (y \rightarrow 1) x$ are considered. The connections these algebras
 various commutative groups (such as, for
 example, involutive moons (weakly)
 goops) described. In particular, it is proved that an RM
 algebra verifying this equivalent to involutive
 moon.
منابع مشابه
Commutative pseudo BE-algebras
The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...
متن کاملNon-commutative Gröbner Bases for Commutative Algebras
An ideal I in the free associative algebra k〈X1, . . . ,Xn〉 over a field k is shown to have a finite Gröbner basis if the algebra defined by I is commutative; in characteristic 0 and generic coordinates the Gröbner basis may even be constructed by lifting a commutative Gröbner basis and adding commutators.
متن کاملCohomology and Obstructions: Commutative Algebras
Associated with each of the classical cohomology theories in algebra has been a theory relating H (H as classically numbered) to obstructions to non-singular extensions and H with coefficients in a “center” to the non-singular extension theory (see [Eilenberg & MacLane (1947), Hochschild (1947), Hochschild (1954), MacLane (1958), Shukla (1961), Harrison (1962)]). In this paper we carry out the ...
متن کاملSimple Graded Commutative Algebras
We study the notion of Γ-graded commutative algebra for an arbitrary abelian group Γ. The main examples are the Clifford algebras already treated in [2]. We prove that the Clifford algebras are the only simple finitedimensional associative graded commutative algebras over R or C. Our approach also leads to non-associative graded commutative algebras extending the Clifford algebras.
متن کاملCommutative combinatorial Hopf algebras
We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general construction based on graphs, and its noncommutative dual is realized in three different ways, in particular, as the Grossman–Larson algebra of heap-ordered trees. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Electronic Journal of Algebra
سال: 2021
ISSN: ['1306-6048']
DOI: https://doi.org/10.24330/ieja.852024