Ideals and Quotients of Diagonally Quasi-Symmetric Functions

IDEALS WITH (d1, . . . , dm)-LINEAR QUOTIENTS

In this paper, we introduce the class of ideals with $(d_1,ldots,d_m)$-linear quotients generalizing the class of ideals with linear quotients. Under suitable conditions we control the numerical invariants of a minimal free resolution of ideals with $(d_1,ldots,d_m)$-linear quotients. In particular we show that their first module of syzygies is a componentwise linear module.

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

Quasi-stability versus Genericity

Quasi-stable ideals appear as leading ideals in the theory of Pommaret bases. We show that quasi-stable leading ideals share many of the properties of the generic initial ideal. In contrast to genericity, quasistability is a characteristic independent property that can be effectively verified. We also relate Pommaret bases to some invariants associated with local cohomology, exhibit the existen...

A CHARACTERIZATION OF BAER-IDEALS

An ideal I of a ring R is called right Baer-ideal if there exists an idempotent e 2 R such that r(I) = eR. We know that R is quasi-Baer if every ideal of R is a right Baer-ideal, R is n-generalized right quasi-Baer if for each I E R the ideal In is right Baer-ideal, and R is right principaly quasi-Baer if every principal right ideal of R is a right Baer-ideal. Therefore the concept of Baer idea...

Fuzzy Soft Quasi-Ideals and Bi-Ideals Over a Right Ternary Near-Ring

Right ternary near-rings (RTNR) are generalization of their binary counterpart and fuzzy soft sets are generalization of soft sets which are parameterized family of subsets of a universal set. In this paper fuzzy soft Nsubgroups, quasi-ideals and bi-ideals over a right ternary near-ring N are defined. The substructures N-subgroups, quasi-ideals and bi-ideals of an RTNR are characterized in term...