The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

For more than two years, we monitored with the HARPS-N spectrograph 400 Myr-old star HD\,63433, which hosts close-in (orbital periods $P_b\sim7.1$ and $P_c\sim20.5$ days) sub-Neptunes detected by TESS space telescope, it was announced in 2020. Using radial velocities additional photometry, aim to provide first measurement of their masses, improve measure size orbital parameters, study evolution...

In the age of JWST, temperate terrestrial exoplanets transiting nearby late-type M dwarfs provide unique opportunities for characterising their atmospheres, as well searching biosignature gases. We report here discovery and validation two super-Earths LP 890-9 (TOI-4306, SPECULOOS-2), a relatively low-activity (32 pc) M6V star. The inner planet, 890-9b, was first detected by TESS (and identifie...

We present the discovery of Kepler-129 d ($P_{d}=7.2^{+0.4}_{-0.3}$ yr, $m\sin i_{d}=8.3^{+1.1}_{-0.7}\ \rm M_{Jup}$, $ e_{d}=0.15^{+0.07}_{-0.05} $) based on six years radial velocity (RV) observations from Keck/HIRES. also hosts two transiting sub-Neptunes: b ($P_{b}=15.79$ days, $r_{b}=2.40\pm{0.04}\ \rm{R_{\oplus}}$) and c ($P_{c}=82.20$ $r_{c}=2.52\pm{0.07}\ for which we measure masses $m_...

We report on the discovery and validation of a two-planet system around bright (V = 8.85 mag) early G dwarf (1.43 $R_{\odot}$, 1.15 $M_{\odot}$, TOI 2319) using data from NASA's Transiting Exoplanet Survey Satellite (TESS). Three transit events two planets were detected by citizen scientists in month-long TESS light curve (sector 25), as part Planet Hunters project. Modelling transits yields an...

let $r$ be a commutative ring. in this paper we assert some properties of finitely generated comultiplication modules and fitting ideals of them.

we show that every semi-artinian module which is contained in a direct sum of finitely presented modules in $si[m]$, is weakly co-semisimple if and only if it is regular in $si[m]$. as a consequence, we observe that every semi-artinian ring is regular in the sense of von neumann if and only if its simple modules are $fp$-injective.

let r be a ring,  be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].

‎A module $M$ is called FI-extending if every fully invariant submodule of $M$ is essential in a direct summand of $M$‎. ‎It is not known whether a direct summand of an FI-extending module is also FI-extending‎. ‎In this study‎, ‎it is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?