Exploring the Structure of Possibility Multi-Fuzzy Soft Ordered Semigroups Through Interior Ideals by Sana Habib, Kashif Habib, Violeta Leoreanu-Fotea, Faiz Muhammad Khan

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Rough Fuzzy Ideals Induced by Set-Valued Homomorphism in Ternary Semigroups by Shahida Bashir, Muhammad Aslam, Rabia Mazhar, Junaid Asghar

“…It is proved that generalized lower approximations and generalized upper approximations of ∈,∈∨q-fuzzy prime (resp., semiprime) ideals of ternary semigroups are ∈,∈∨q-fuzzy prime (resp., semiprime) ideals. …”
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Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-Ideals by Jian Tang, Xiangyun Xie, Yanfeng Luo

“…In addition, we also introduce the concepts of prime and completely semiprime interval valued (∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals of ordered semigroups and characterize bi-regular ordered semigroups in terms of completely semiprime interval valued (∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals. …”
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Generalized roughness of three dimensional ( $$\in ,\in \vee q$$ ∈ , ∈ ∨ q )-fuzzy ideals in terms of set-valued homomorphism by Shahida Bashir, Rabia Mazhar, Nasreen Kausar, Saziye Yaman, Syed Suleman Ali, Muneeb Ul Hassan Afzal

“…By using the concept of set-valued homomorphism and strong set-valued homomorphism, it is proved generalized lower and upper approximations of $$(\in , \in \vee q)$$ ( ∈ , ∈ ∨ q ) -fuzzy ideals (semiprime and prime ideals) of ternary semirings are $$(\in ,\in \vee q)$$ ( ∈ , ∈ ∨ q ) -fuzzy ideals (semiprime and prime ideals) respectively.…”
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Jordan superderivations. II by Maja Fošner

“…In the present paper we extend this result to semiprime associative superalgebras.…”
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Concave Soft Sets, Critical Soft Points, and Union-Soft Ideals of Ordered Semigroups by Young Bae Jun, Seok Zun Song, G. Muhiuddin

“…The concepts of union-soft products and union-soft semiprime soft sets are introduced, and their properties related to union-soft l-ideals and union-soft r-ideals are investigated. …”
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On quasi-ideals of semirings by Christoph Dönges

“…In particular, if the considered semiring S is semiprime or quasi-reflexive, we present criterions which allow to decide easily whether an (O−)minimal quasi-ideal of S is canonical (cf. …”
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Factor Rings with Algebraic Identities via Generalized Derivations by Ali Yahya Hummdi, Zakia Z. Al-Amery, Radwan M. Al-omary

“…These derivations satisfy specific differential identities involving <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Π</mo></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Π</mo></semantics></math></inline-formula> is a prime ideal of an arbitrary ring <i>ℜ</i>, not necessarily prime or semiprime. Furthermore, we explore some consequences of our findings. …”
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Soft intersection almost bi-quasi-interior ideals of semigroups by Aslıhan Sezgin, Zeynep BAŞ, Aleyna İlgin

“…With this vital theorem, several interesting relationships between certain types of almost BQI-ideals of semigroups, such as minimal, prime, semiprime, and strongly prime almost BQI-ideals and certain types of soft intersection almost BQI-ideals, are derived.  …”
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New proof and generalization of some results on translated sums over k-almost primes by Laib, Ilias

“…In 2019, Laib et al. proved that the analogous conjecture of Erdős $f(\mathcal{A},h)\le f(\mathbb{N}_{1},h)$ is false for $h\ge 81$ on a sequence of semiprimes. Recently, Lichtman gave the best lower bound $h=1.04\cdots $ on semiprimes and he obtained other results for translated sums on $k$-almost primes with $ 2…”
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