the left regular representation of a commutative separative semigroup
نویسندگان
چکیده
in this paper, a commutative semigroup will be written as a disjoint :union: of its cancellative subsemigroups. based on this fact we will define the left regular representation of a commutative separative semigroup and show that this representation is faithful. finally concrete examples of commutative separative semigroups, their decompositions and their left regular representations are given.
منابع مشابه
THE LEFT REGULAR REPRESENTATION OF A COMMUTATIVE SEPARATIVE SEMIGROUP
In this paper, a commutative semigroup will be written as a disjoint union of its cancellative subsemigroups. Based on this fact we will define the left regular representation of a commutative separative semigroup and show that this representation is faithful. Finally concrete examples of commutative separative semigroups, their decompositions and their left regular representations are given.
متن کاملTHE DUALITY OF THE L?-REPRESENTATION ALGEBRA ?(S ) OF A FOUNDATION SEMIGROUP S AND FUNCTION ALGEBRAS
In the present paper for a large family of topological semigroups, namely foundation semigroups, for which topological groups and discrete semigroups are elementary examples, it is shown that ?(S) is the dual of a function algebra.
متن کاملThe Quiver of the Semigroup Algebra of a Left Regular Band
Recently it has been noticed that many interesting combinatorial objects belong to a class of semigroups called left regular bands, and that random walks on these semigroups encode several well-known random walks. For example, the set of faces of a hyperplane arrangement is endowed with a left regular band structure. This paper studies the module structure of the semigroup algebra of an arbitra...
متن کاملOn the Imbedding of a Finite Commutative Semigroup of Idempotents in a Uniquely Factorable Semigroup.
A semigroup is a set of elements to which is related an operation usually called multiplication and an equivalence relation, such that the set is closed and associative relative to the operation. We shall discuss, briefly, finite semigroups which are uniquely factorable in the same sense as the multiplicative semigroup of all nonzero integers. Clifford' defined an arithmetic in such a way as to...
متن کاملOn the Multiplicative Semigroup of a Commutative Ring
There seems to be no approach in the literature to a general theory of the structural restrictions which a semigroup must satisfy to be the multiplicative part of a ring. Johnson has treated the case that, as in Boolean rings, the addition is uniquely determined by the multiplication [l]. I do not know whether the present theorem extends to the noncommutative case. I am indebted to John Rainwat...
متن کاملStability in the Cuntz Semigroup of a Commutative C-algebra
Let A be a C-algebra. The Cuntz semigroup W (A) is an analogue for positive elements of the semigroup V (A) of Murray-von Neumann equivalence classes of projections in matrices over A. We prove stability theorems for the Cuntz semigroup of a commutative C-algebra which are analogues of classical stability theorems for topological vector bundles over compact Hausdorff spaces. Let SDG denote the ...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
journal of sciences islamic republic of iranجلد ۳، شماره ۲، صفحات ۰-۰
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023