The closed one-sided ideals of a C-algebra are exactly the closed subspaces supported by the orthogonal complement of a closed projection. Let A be a (not necessarily selfadjoint) subalgebra of a unital C-algebra B which contains the unit of B. Here we characterize the right ideals of A with left contractive approximate identity as those subspaces of A supported by the orthogonal complement of ...

We further explore the idea that physics takes place in Clifford space which should be considered as a generalization of spacetime. Following the old observation that spinors can be represented as members of left ideals of Clifford algebra, we point out that the transformations which mix bosons and fermions could be represented by means of operators acting on Clifford algebra-valued (polyvector...

In this note, we show that an ordered ternary semigroup is left and right simple if and only if it does not contain proper bi-ideals. The similar result is valid on ordered semigroups [7], on ordered Γ-semigroups [3] and on ternary semigroups [4]. Mathematics Subject Classification: 06F05

Let $F$ be a non-negatively graded free module over polynomial ring $\mathbb{K}[x_1,\dots,x_n]$ generated by $m$ basis elements. $M$ submodule of elements in with degrees bounded $D$ and dim $F/M$=$r$. We prove that if is graded, the degree reduced Gr\"{o}bner for any term order $2\left[1/2((Dm)^{n-r}m+D) \right]^{2^{r-1}}$. If not bound $2\left[1/2((Dm)^{(n-r)^2}m+D) \right]^{2^{r}}$. This gen...

multi fuzzy set theory is an extension of theory, which deals with the dimensional fuzziness. In this paper, we introduce concepts multi-fuzzy rings, ideal, image multi- ideal a ring under homomorphism, Cartesian product set, and some related properties theorems are investigated. The purpose study to implement rings in rings.

a Department of Mathematics and Statistics, International Islamic University Islamabad, Pakistan. b Department of Mathematics, Riphah International University Islamabad, Pakistan.  Corresponding Author's Email: [email protected] ABSTRACT: In this paper, we introduce the notions of soft intersectional ternary subsemirings and soft intersectional ideals in ternary semirings. We also discuss ...

From the combinatorial characterizations of the right, left, and two-sided Kazhdan-Lusztig cells of the symmetric group, ‘KRS bases’ are constructed for certain quotients by two-sided ideals of the group ring and the Hecke algebra. Applications to invariant theory of the general linear group and representation theory of the symmetric group are discussed.

The representations of some Hopf algebras have curious behavior: Nonprojective modules may have projective tensor powers, and the variety of a tensor product of modules may not be contained in the intersection of their varieties. We explain a family of examples of such Hopf algebras and their modules, and classify left, right, and two-sided ideals in their stable module categories.